메뉴 건너뛰기




Volumn 1893, Issue , 2007, Pages 1-235

Local and semi-local bifurcations in hamiltonian dynamical systems: Results and examples

Author keywords

[No Author keywords available]

Indexed keywords


EID: 85072837579     PISSN: 00758434     EISSN: 16179692     Source Type: Book Series    
DOI: None     Document Type: Chapter
Times cited : (75)

References (299)
  • 1
    • 0001626493 scopus 로고
    • Asymptotic integrability and periodic solutions of a Hamiltonian system in 1:2:2-resonance
    • p
    • E. van der Aa and F. Verhulst: Asymptotic integrability and periodic solutions of a Hamiltonian system in 1:2:2-resonance; SIAM J. Math. Anal. 15(5), p. 890–911 (1984)
    • (1984) SIAM J. Math. Anal. , vol.15 , Issue.5 , pp. 890-911
    • van der Aa, E.1    Verhulst, F.2
  • 2
    • 0028400752 scopus 로고
    • Systems in 1:2:ω-resonance (ω = 5 or 6)
    • p
    • E. van der Aa and M. de Winkel: Systems in 1:2:ω-resonance (ω = 5 or 6); Int. J. Non-Lin. Mech. 29(2), p. 261–270 (1994)
    • (1994) Int. J. Non-Lin. Mech. , vol.29 , Issue.2 , pp. 261-270
    • van der Aa, E.1    de Winkel, M.2
  • 5
    • 0002764805 scopus 로고
    • Proof of a theorem of A. N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian
    • p
    • V.I. Arnol’d: Proof of a theorem of A. N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian; Russ. Math. Surv. 18(5), p. 9–36 (1963)
    • (1963) Russ. Math. Surv. , vol.18 , Issue.5 , pp. 9-36
    • Arnol’D, V.I.1
  • 6
    • 0002356196 scopus 로고
    • Small denominators and problems of stability of motion in classical and celestial mechanics
    • p
    • V.I. Arnol’d: Small denominators and problems of stability of motion in classical and celestial mechanics; Russ. Math. Surv. 18(6), p. 85–191 (1963)
    • (1963) Russ. Math. Surv. , vol.18 , Issue.6 , pp. 85-191
    • Arnol’D, V.I.1
  • 7
    • 0000877933 scopus 로고
    • D: Instability of dynamical systems with several degrees of freedom
    • p
    • V.I. Arnol’d: Instability of dynamical systems with several degrees of freedom; Sov. Math. Dokl. 5, p. 581–585 (1964)
    • (1964) Sov. Math. Dokl , vol.5 , pp. 581-585
    • Arnol, I.1
  • 8
    • 84927914894 scopus 로고
    • On matrices depending on parameters
    • p
    • V.I. Arnol’d: On matrices depending on parameters; Russ. Math. Surv. 26(2), p. 29–43 (1971)
    • (1971) Russ. Math. Surv. , vol.26 , Issue.2 , pp. 29-43
    • Arnol’D, V.I.1
  • 9
    • 0039870884 scopus 로고
    • k, and Lagrangian singularities
    • p
    • k, and Lagrangian singularities; Funct. Anal. Appl. 6, p. 254–272 (1972)
    • (1972) Funct. Anal. Appl , vol.6 , pp. 254-272
    • Arnol, I.1
  • 10
    • 84957144486 scopus 로고
    • Normal forms of functions in neighbourhoods of degenerate critical points; Russ
    • p
    • V.I. Arnol’d: Normal forms of functions in neighbourhoods of degenerate critical points; Russ. Math. Surv. 29(2), p. 11–49 (1974)
    • (1974) Math. Surv. , vol.29 , Issue.2 , pp. 11-49
    • Arnol’D, V.I.1
  • 11
    • 84950562602 scopus 로고
    • Critical points of smooth functions and their normal forms
    • p
    • V.I. Arnol’d: Critical points of smooth functions and their normal forms; Russ. Math. Surv. 30(5), p. 1–75 (1975)
    • (1975) Russ. Math. Surv. , vol.30 , Issue.5 , pp. 1-75
    • Arnol’D, V.I.1
  • 14
    • 85072840745 scopus 로고
    • Shil’nikov: Bifurcation Theory; Part I in Dynamical Systems V (ed. V.I. Arnol’d) Springer
    • V.I. Arnol’d, V.S. Afrajmovich, Yu.S. Il’yashenko and L.P. Shil’nikov: Bifurcation Theory; Part I in Dynamical Systems V (ed. V.I. Arnol’d) Springer (1993)
    • (1993) Yu.S. Il’yashenko and L.P
    • Arnol’D, V.I.1    Afrajmovich, V.S.2
  • 16
    • 85072837518 scopus 로고
    • Neishtadt: Mathematical Aspects of Classical and Celestial Mechanics; in Dynamical Systems III (ed. V.I. Arnol’d) Springer
    • V.I. Arnol’d, V.V. Kozlov and A.I. Neishtadt: Mathematical Aspects of Classical and Celestial Mechanics; in Dynamical Systems III (ed. V.I. Arnol’d) Springer (1988)
    • (1988) V.V. Kozlov and A.I
    • Arnol’D, V.I.1
  • 17
    • 85072836049 scopus 로고
    • Singularity theory I: Singularities, local and global theory; in Dynamical Systems VI (ed. V.I. Arnol’d) Springer
    • V.I. Arnol’d, V.A. Vasil’ev, V.V.Goryunov and O.V. Lyashko: Singularity theory I: Singularities, local and global theory; in Dynamical Systems VI (ed. V.I. Arnol’d) Springer (1993)
    • (1993) V.V.Goryunov and O.V. Lyashko
    • Arnol’D, V.I.1    Vasil’Ev, V.A.2
  • 20
    • 0000200040 scopus 로고
    • Degeneration of Hamiltonian monodromy cycles
    • p
    • L. Bates and M. Zou: Degeneration of Hamiltonian monodromy cycles; Nonlinearity 6(2), p. 313–335 (1993)
    • (1993) Nonlinearity , vol.6 , Issue.2 , pp. 313-335
    • Bates, L.1    Zou, M.2
  • 21
    • 85072839121 scopus 로고
    • Endliche Bestimmtheit und universelle Entfaltungen von Keimen mit Gruppenoperation; Diplomarbeit, Universität
    • M. Beer: Endliche Bestimmtheit und universelle Entfaltungen von Keimen mit Gruppenoperation; Diplomarbeit, Universität Regensburg (1976)
    • (1976) Regensburg
    • Beer, M.1
  • 24
    • 85072834985 scopus 로고
    • Construction of Invariant Tori of Systems of Differential Equations with a Small Parameter
    • p
    • Yu.N. Bibikov: Construction of Invariant Tori of Systems of Differential Equations with a Small Parameter; Transl. AMS, Ser.2 155, p. 19–46, (1993)
    • (1993) Transl. AMS, Ser. , vol.2 , Issue.155 , pp. 19-46
    • Bibikov, Y.N.1
  • 25
    • 0002447210 scopus 로고
    • Nouvelles recherches sur les systemes dynamiques; Mem
    • p
    • B.D. Birkhoff: Nouvelles recherches sur les systemes dynamiques; Mem. Pont. Acad. Sci. Novi Lyncaei, Ser.3 1, p. 85–216 (1935)
    • (1935) Pont. Acad. Sci. Novi Lyncaei, Ser , vol.3 , Issue.1 , pp. 85-216
    • Birkhoff, B.D.1
  • 26
    • 0009181928 scopus 로고
    • What is the ergodic theorem
    • p
    • B.D. Birkhoff: What is the ergodic theorem; Amer. Math. Monthly 49, p. 222–226 (1942)
    • (1942) Amer. Math. Monthly , vol.49 , pp. 222-226
    • Birkhoff, B.D.1
  • 28
    • 0012910628 scopus 로고    scopus 로고
    • Remarks on the definition of hyperbolic tori of Hamiltonian systems
    • p
    • S.V. Bolotin and D.V. Treschëv: Remarks on the definition of hyperbolic tori of Hamiltonian systems; Reg. & Chaot. Dyn. 5(4), p. 401–412 (2000)
    • (2000) Reg. & Chaot. Dyn. , vol.5 , Issue.4 , pp. 401-412
    • Bolotin, S.V.1    Treschëv, D.V.2
  • 29
    • 0001486079 scopus 로고
    • Whitney’s extension theorem for nonquasianalytic classes of ultradifferentiable functions
    • p
    • J. Bonet, R.W. Braun, R. Meise and B.A. Taylor: Whitney’s extension theorem for nonquasianalytic classes of ultradifferentiable functions; Studia Math. 99(2), p.155–184 (1991)
    • (1991) Studia Math , vol.99 , Issue.2 , pp. 155-184
    • Bonet, J.1    Braun, R.W.2    Meise, R.3    Taylor, B.A.4
  • 30
    • 84963026889 scopus 로고
    • Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE
    • p
    • J. Bourgain: Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE; Int. Math. Res. Notices 1994(11), p. 475–497 (1994)
    • (1994) Int. Math. Res. Notices , vol.1994 , Issue.11 , pp. 475-497
    • Bourgain, J.1
  • 31
    • 0031287692 scopus 로고    scopus 로고
    • On Melnikov’s persistency problem
    • p
    • J. Bourgain: On Melnikov’s persistency problem; Math. Res. Lett. 4, p. 445– 458 (1997)
    • (1997) Math. Res. Lett. , vol.4 , pp. 445-458
    • Bourgain, J.1
  • 32
    • 85072838410 scopus 로고
    • Quasiperiodic flow near a codimension one singularity of a divergence free vector field in dimension four; p. 74–142 in bifurcation, théorie ergodique et applications, Dijon 1981 (ed. Anonymous)
    • B.J.L. Braaksma and H.W. Broer: Quasiperiodic flow near a codimension one singularity of a divergence free vector field in dimension four; p. 74–142 in bifurcation, théorie ergodique et applications, Dijon 1981 (ed. Anonymous), Astérisque 98-99 (1982)
    • (1982) Astérisque , pp. 98-99
    • Braaksma, B.J.L.1    Broer, H.W.2
  • 35
    • 0000639077 scopus 로고
    • Bifurcation of periodic solutions near a collision of eigenvalues of opposite signature
    • p
    • T.J. Bridges: Bifurcation of periodic solutions near a collision of eigenvalues of opposite signature; Math. Proc. Camb. Phil. Soc. 108, p. 575–601 (1990)
    • (1990) Math. Proc. Camb. Phil. Soc. , vol.108 , pp. 575-601
    • Bridges, T.J.1
  • 36
    • 84974324339 scopus 로고
    • Stability of periodic solutions near a collision of eigenvalues of opposite signature
    • p
    • T.J. Bridges: Stability of periodic solutions near a collision of eigenvalues of opposite signature; Math. Proc. Camb. Phil. Soc. 109, p. 375–403 (1991)
    • (1991) Math. Proc. Camb. Phil. Soc. , vol.109 , pp. 375-403
    • Bridges, T.J.1
  • 37
    • 85072837638 scopus 로고
    • Dynamics near an Irrational Collision of Eigenvalues for Symplectic Mappings; p. 61–79 in Normal Forms and Homoclinic Chaos, Waterloo 1992 (eds. W.F. Langford and W
    • T.J. Bridges, R.H. Cushman and R.S. MacKay: Dynamics near an Irrational Collision of Eigenvalues for Symplectic Mappings; p. 61–79 in Normal Forms and Homoclinic Chaos, Waterloo 1992 (eds. W.F. Langford and W. Nagata) Fields Institute Communications 4 AMS (1995)
    • (1995) Nagata) Fields Institute Communications 4 AMS
    • Bridges, T.J.1    Cushman, R.H.2    Mackay, R.S.3
  • 39
    • 0040826888 scopus 로고
    • Die Hierarchie der 1-modularen Singularitäten
    • p
    • E. Brieskorn: Die Hierarchie der 1-modularen Singularitäten; Manuscr. Math. 27, p. 183–219 (1979)
    • (1979) Manuscr. Math. , vol.27 , pp. 183-219
    • Brieskorn, E.1
  • 48
    • 85072829431 scopus 로고    scopus 로고
    • p., in: Dynamics & Stochastics: Festschrift in Honor of M.S. Keane (eds. D. Denteneer, F. den Hollander and E. Verbitskiy) Lecture Notes 48, Inst. of Math. Statistics
    • H.W. Broer, H. Hanßmann, J. Hoo and V. Naudot: Nearly-integrable perturbations of the Lagrange top: applications of KAM-theory; p. 286–303 in: Dynamics & Stochastics: Festschrift in Honor of M.S. Keane (eds. D. Denteneer, F. den Hollander and E. Verbitskiy) Lecture Notes 48, Inst. of Math. Statistics (2006)
    • (2006) Nearly-Integrable Perturbations of the Lagrange Top: Applications of Kam-Theory , pp. 286-303
    • Broer, H.W.1    Hanßmann, H.2    Hoo, J.3    Naudot, V.4
  • 49
    • 0142137606 scopus 로고    scopus 로고
    • Normal-internal resonances in quasi-periodically forced oscillators: A conservative approach
    • p
    • H.W. Broer, H. Hanßmann, À. Jorba, J. Villanueva and F.O.O. Wagener: Normal-internal resonances in quasi-periodically forced oscillators: a conservative approach; Nonlinearity 16, p. 1751–1791 (2003)
    • (2003) Nonlinearity , vol.16 , pp. 1751-1791
    • Broer, H.W.1    Hanßmann, H.2    Jorba, À.3    Villanueva, J.4    Wagener, F.O.O.5
  • 50
    • 21244442290 scopus 로고    scopus 로고
    • Bifurcations of normally parabolic tori in Hamiltonian systems
    • p
    • H.W. Broer, H. Hanßmann and J. You: Bifurcations of normally parabolic tori in Hamiltonian systems; Nonlinearity 18, p. 1735–1769 (2005)
    • (2005) Nonlinearity , vol.18 , pp. 1735-1769
    • Broer, H.W.1    Hanßmann, H.2    You, J.3
  • 51
    • 32044436274 scopus 로고    scopus 로고
    • Umbilical Torus Bifurcations in Hamiltonian Systems
    • p
    • H.W. Broer, H. Hanßmann and J. You: Umbilical Torus Bifurcations in Hamiltonian Systems; J. Diff. Eq. 222, p. 233–262 (2006)
    • (2006) J. Diff. Eq. , vol.222 , pp. 233-262
    • Broer, H.W.1    Hanßmann, H.2    You, J.3
  • 52
    • 85072823953 scopus 로고    scopus 로고
    • Normal Linear Stability of Quasi-Periodic Tori
    • to appear
    • H.W. Broer, J. Hoo and V. Naudot: Normal Linear Stability of Quasi-Periodic Tori; J. Diff. Eq. (to appear)
    • J. Diff. Eq.
    • Broer, H.W.1    Hoo, J.2    Naudot, V.3
  • 54
    • 0002321444 scopus 로고
    • A proof of the isoenergetic KAM-theorem from the “ordinary” one
    • p
    • H.W. Broer and G.B. Huitema: A proof of the isoenergetic KAM-theorem from the “ordinary” one; J. Diff. Eq. 90(1), p. 52–60 (1991)
    • (1991) J. Diff. Eq. , vol.90 , Issue.1 , pp. 52-60
    • Broer, H.W.1    Huitema, G.B.2
  • 57
    • 22244480073 scopus 로고    scopus 로고
    • Equivariant singularity theory with distinguished parameters: Two case studies of resonant Hamiltonian systems
    • in Time-reversal symmetry in dynamical systems, Warwick 1996 (ed. J.S.W. Lamb)
    • H.W. Broer, G. Lunter and G. Vegter: Equivariant singularity theory with distinguished parameters: Two case studies of resonant Hamiltonian systems; p. 64–80 in Time-reversal symmetry in dynamical systems, Warwick 1996 (ed. J.S.W. Lamb), Physica D 112 (1998)
    • (1998) Physica D , vol.112 , pp. 64-80
    • Broer, H.W.1    Lunter, G.2    Vegter, G.3
  • 58
    • 0030355090 scopus 로고    scopus 로고
    • Invariant circles in the Bogdanov– Takens bifurcation for diffeomorphisms
    • p
    • H.W. Broer, R. Roussarie and C. Simó: Invariant circles in the Bogdanov– Takens bifurcation for diffeomorphisms; Erg.Th.Dyn.Syst.16, p. 1147–1172 (1996)
    • (1996) Erg.Th.Dyn.Syst. , vol.16 , pp. 1147-1172
    • Broer, H.W.1    Roussarie, R.2    Simó, C.3
  • 60
    • 53149138221 scopus 로고    scopus 로고
    • Integrable and non-integrable deformations of the skew-Hopf bifurcation
    • p
    • H.W. Broer, F. Takens and F.O.O. Wagener: Integrable and non-integrable deformations of the skew-Hopf bifurcation; Reg. & Chaot. Dyn. 4(2), p. 17–43 (1999)
    • (1999) Reg. & Chaot. Dyn. , vol.4 , Issue.2 , pp. 17-43
    • Broer, H.W.1    Takens, F.2    Wagener, F.O.O.3
  • 61
    • 0002208766 scopus 로고
    • Bifurcational Aspects of Parametric Resonance
    • p
    • H.W. Broer and G. Vegter: Bifurcational Aspects of Parametric Resonance; Dynamics Rep., new ser. 1, p. 1–53 (1992)
    • (1992) Dynamics Rep., New Ser. , vol.1 , pp. 1-53
    • Broer, H.W.1    Vegter, G.2
  • 62
    • 0034409608 scopus 로고    scopus 로고
    • Quasi-periodic stability of subfamilies of an unfolded skew-Hopf bifurcation
    • p
    • H.W. Broer and F.O.O. Wagener: Quasi-periodic stability of subfamilies of an unfolded skew-Hopf bifurcation; Arch. Rat. Mech. An. 152, p. 283–326 (2000)
    • (2000) Arch. Rat. Mech. An. , vol.152 , pp. 283-326
    • Broer, H.W.1    Wagener, F.O.O.2
  • 63
    • 84875993856 scopus 로고    scopus 로고
    • Time-reversible Hamiltonian vector fields with symplectic symmetries
    • p
    • C.A. Buzzi and M.A. Teixeira: Time-reversible Hamiltonian vector fields with symplectic symmetries; J. Dynamics Diff. Eq. 16, p. 559–574 (2004)
    • (2004) J. Dynamics Diff. Eq. , vol.16 , pp. 559-574
    • Buzzi, C.A.1    Teixeira, M.A.2
  • 64
    • 0033196541 scopus 로고    scopus 로고
    • Stability of equilibria and fixed points of conservative systems
    • p
    • H.E. Cabral and K.E. Meyer: Stability of equilibria and fixed points of conservative systems; Nonlinearity 12, p. 1351–1362 (1999)
    • (1999) Nonlinearity , vol.12 , pp. 1351-1362
    • Cabral, H.E.1    Meyer, K.E.2
  • 65
    • 51649147118 scopus 로고
    • Bifurcations des points elliptiques-I. Courbes invariantes
    • p
    • A. Chenciner: Bifurcations des points elliptiques-I. Courbes invariantes; Publ. Math., Inst. Hautes Etud. Sci. 61, p. 67–127 (1985)
    • (1985) Publ. Math., Inst. Hautes Etud. Sci. , vol.61 , pp. 67-127
    • Chenciner, A.1
  • 66
    • 0013369791 scopus 로고
    • Bifurcations des points elliptiques-II. Orbites périodiques et ensembles de Cantor invariants
    • p
    • A. Chenciner: Bifurcations des points elliptiques-II. Orbites périodiques et ensembles de Cantor invariants; Inv. Math. 80, p. 81–106 (1985)
    • (1985) Inv. Math. , vol.80 , pp. 81-106
    • Chenciner, A.1
  • 67
    • 51649147531 scopus 로고
    • Bifurcations des points elliptiques-III. Orbites périodiques de “petites” périodes et élimination résonnante des couples de courbes invariantes
    • p
    • A. Chenciner: Bifurcations des points elliptiques-III. Orbites périodiques de “petites” périodes et élimination résonnante des couples de courbes invariantes; Publ. Math., Inst. Hautes Etud. Sci. 66, p. 5–91 (1987)
    • (1987) Publ. Math., Inst. Hautes Etud. Sci. , vol.66 , pp. 5-91
    • Chenciner, A.1
  • 68
    • 0007142221 scopus 로고
    • Bifurcations de tores invariants
    • p
    • A. Chenciner and G. Iooss: Bifurcations de tores invariants; Arch. Rat. Mech. An. 69(2), p. 109–198 (1979)
    • (1979) Arch. Rat. Mech. An. , vol.69 , Issue.2 , pp. 109-198
    • Chenciner, A.1    Iooss, G.2
  • 69
    • 0040799578 scopus 로고    scopus 로고
    • Birkhoff–Kolmogorov–Arnold–Moser tori in convex Hamiltonian systems
    • p
    • C.-Q. Cheng: Birkhoff–Kolmogorov–Arnold–Moser tori in convex Hamiltonian systems; Comm. Math. Phys. 177, p. 529–559 (1996)
    • (1996) Comm. Math. Phys. , vol.177 , pp. 529-559
    • Cheng, C.-Q.1
  • 70
    • 0039726729 scopus 로고    scopus 로고
    • Lower Dimensional Invariant Tori in the Regions of Instability for Nearly Integrable Hamiltonian Systems
    • p
    • C.-Q. Cheng: Lower Dimensional Invariant Tori in the Regions of Instability for Nearly Integrable Hamiltonian Systems; Comm. Math. Phys. 203, p. 385– 419 (1999)
    • (1999) Comm. Math. Phys. , vol.203 , pp. 385-419
    • Cheng, C.-Q.1
  • 71
    • 0000692506 scopus 로고
    • A direct proof of a Theorem by Kolmogorov in Hamiltonian Systems
    • p
    • L. Chierchia and C. Falcolini: A direct proof of a Theorem by Kolmogorov in Hamiltonian Systems; Ann. Sc. Norm. Sup. Pisa, Cl. Sci., Ser.IV 21(4), p. 541–593 (1994)
    • (1994) Ann. Sc. Norm. Sup. Pisa, Cl. Sci., Ser.Iv , vol.21 , Issue.4 , pp. 541-593
    • Chierchia, L.1    Falcolini, C.2
  • 72
    • 52449147455 scopus 로고
    • Smooth prime integrals for quasi-integrable Hamiltonian systems
    • p
    • L. Chierchia and G. Gallavotti: Smooth prime integrals for quasi-integrable Hamiltonian systems; Nuovo Cimento B 67, p. 277–295 (1982)
    • (1982) Nuovo Cimento B , vol.67 , pp. 277-295
    • Chierchia, L.1    Gallavotti, G.2
  • 73
    • 4544242704 scopus 로고    scopus 로고
    • Moser’s theorem for lower dimensional tori
    • p
    • L. Chierchia and D. Qian: Moser’s theorem for lower dimensional tori; J. Diff. Eq. 206(1), p. 55–93 (2004)
    • (2004) J. Diff. Eq. , vol.206 , Issue.1 , pp. 55-93
    • Chierchia, L.1    Qian, D.2
  • 74
    • 0001556435 scopus 로고
    • On Averaging, Reduction, and Symmetry in Hamiltonian Systems
    • p
    • R.C. Churchill, M. Kummer and D.L. Rod: On Averaging, Reduction, and Symmetry in Hamiltonian Systems; J. Diff. Eq. 49, p. 359–414 (1983)
    • (1983) J. Diff. Eq. , vol.49 , pp. 359-414
    • Churchill, R.C.1    Kummer, M.2    Rod, D.L.3
  • 78
    • 0011605539 scopus 로고
    • Ph.D. thesis, University of California at Santa Cruz
    • C. Cotter: The 1:1 semisimple resonance; Ph.D. thesis, University of California at Santa Cruz (1986)
    • (1986) The 1:1 Semisimple Resonance
    • Cotter, C.1
  • 79
    • 84867039153 scopus 로고
    • Varieties and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra; Springer
    • D. Cox, J. Little and D. O’Shea: Ideals, Varieties and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra; Springer (1992)
    • (1992) Ideals
    • Cox, D.1    Little, J.2    O’Shea, D.3
  • 80
    • 0009206017 scopus 로고
    • A Survey of Normalization Techniques Applied to Perturbed Keplerian Systems
    • p
    • R. Cushman: A Survey of Normalization Techniques Applied to Perturbed Keplerian Systems; Dynamics Rep., new ser. 1, p. 54–112 (1992)
    • (1992) Dynamics Rep., New Ser. , vol.1 , pp. 54-112
    • Cushman, R.1
  • 83
    • 0033099574 scopus 로고    scopus 로고
    • Singular reduction of axially symmetric perturbations of the isotropic harmonic oscillator
    • p
    • R. Cushman, S. Ferrer and H. Hanßmann: Singular reduction of axially symmetric perturbations of the isotropic harmonic oscillator; Nonlinearity 12, p. 389–410 (1999)
    • (1999) Nonlinearity , vol.12 , pp. 389-410
    • Cushman, R.1    Ferrer, S.2    Hanßmann, H.3
  • 84
    • 85072835090 scopus 로고    scopus 로고
    • in Géométrie Symplectique et Mécanique, La Grande Motte 1988 (ed. C. Albert) LNM 1416, Springer (1990)
    • R. Cushman and J.C. van der Meer: The Hamiltonian Hopf bifurcation in the Lagrange top; p. 26–38 in Géométrie Symplectique et Mécanique, La Grande Motte 1988 (ed. C. Albert) LNM 1416, Springer (1990)
    • The Hamiltonian Hopf Bifurcation in the Lagrange Top , pp. 26-38
    • Cushman, R.1    van der Meer, J.C.2
  • 86
    • 85072846337 scopus 로고    scopus 로고
    • in Oscillation, Bifurcation and Chaos, Toronto 1986 (eds. F.V. Atkinson, W.F. Langford and A.B. Mingarelli), CMS Conference Proceedings 8, AMS (1987)
    • R. Cushman and J. Sanders: Invariant Theory and Normal Form of Hamiltonian Vectorfields with Nilpotent Linear Part; p. 353–371 in Oscillation, Bifurcation and Chaos, Toronto 1986 (eds. F.V. Atkinson, W.F. Langford and A.B. Mingarelli), CMS Conference Proceedings 8, AMS (1987)
    • Invariant Theory and Normal Form of Hamiltonian Vectorfields with Nilpotent Linear Part , pp. 353-371
    • Cushman, R.1    Sanders, J.2
  • 89
    • 85072835384 scopus 로고    scopus 로고
    • On the number of periodic solutions of an Hamiltonian system near an equilibrium point
    • (6) 3-B, p. 809–835 (1984)
    • G.F. Dell’Antonio and B.M. D’Onofrio: On the number of periodic solutions of an Hamiltonian system near an equilibrium point; Boll. U.M.I.(6) 3-B, p. 809–835 (1984)
    • Boll. U.M.I
    • Dell’Antonio, G.F.1    D’Onofrio, B.M.2
  • 90
    • 16244394539 scopus 로고    scopus 로고
    • A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: Announcement of results
    • p
    • A. Delshams, R. dela Llaveand T. Martínez-Seara: A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: announcement of results; Electron. Res. Announc. AMS 9, p. 125–134 (2003)
    • (2003) Electron. Res. Announc. AMS , vol.9 , pp. 125-134
    • Delshams, A.1    Dela Llaveand, R.2    Martínez-Seara, T.3
  • 92
    • 0000467293 scopus 로고
    • Stability of the Lagrange points
    • p
    • A. Deprit and A. Deprit-Bartholomé: Stability of the Lagrange points; Astron. J. 72, p. 173–179 (1967)
    • (1967) Astron. J , vol.72 , pp. 173-179
    • Deprit, A.1    Deprit-Bartholomé, A.2
  • 93
    • 84980174402 scopus 로고
    • Oscillatory integrals, Lagrange immersions, and unfoldings of singularities
    • p
    • J.J. Duistermaat: Oscillatory integrals, Lagrange immersions, and unfoldings of singularities; Comm. Pure Appl. Math. 27, p. 207–281 (1974)
    • (1974) Comm. Pure Appl. Math. , vol.27 , pp. 207-281
    • Duistermaat, J.J.1
  • 95
    • 0002018756 scopus 로고
    • Non-integrability of the 1:1:2-resonance
    • p
    • J.J. Duistermaat: Non-integrability of the 1:1:2-resonance; Ergod. Th. & Dynam. Sys. 4, p. 553–568 (1984)
    • (1984) Ergod. Th. & Dynam. Sys. , vol.4 , pp. 553-568
    • Duistermaat, J.J.1
  • 96
    • 0032340303 scopus 로고    scopus 로고
    • The monodromy of the Hamiltonian Hopf bifurcation
    • p
    • J.J. Duistermaat: The monodromy of the Hamiltonian Hopf bifurcation; Z. angew. Math. Phys. 49, p. 156–161 (1998)
    • (1998) Z. Angew. Math. Phys. , vol.49 , pp. 156-161
    • Duistermaat, J.J.1
  • 98
    • 1142304405 scopus 로고    scopus 로고
    • Monodromy in the resonant swing spring
    • p
    • H.R. Dullin, A. Giacobbe and R. Cushman: Monodromy in the resonant swing spring; Physica D 190, p. 15–37 (2004)
    • (2004) Physica D , vol.190 , pp. 15-37
    • Dullin, H.R.1    Giacobbe, A.2    Cushman, R.3
  • 99
    • 13244277750 scopus 로고    scopus 로고
    • Vanishing twist in the Hamiltonian Hopf bifurcation
    • p
    • H.R. Dullin and A.V. Ivanov: Vanishing twist in the Hamiltonian Hopf bifurcation; Physica D 201, p. 27–44 (2005)
    • (2005) Physica D , vol.201 , pp. 27-44
    • Dullin, H.R.1    Ivanov, A.V.2
  • 100
    • 27144459862 scopus 로고    scopus 로고
    • Another look at the saddle-centre bifurcation: Vanishing twist
    • p
    • H.R. Dullin and A.V. Ivanov: Another look at the saddle-centre bifurcation: Vanishing twist; Physica D 211, p. 47–56 (2005)
    • (2005) Physica D , vol.211 , pp. 47-56
    • Dullin, H.R.1    Ivanov, A.V.2
  • 101
    • 85072830894 scopus 로고    scopus 로고
    • Normal Forms for Symplectic Maps with Twist Singularities; preprint #2134/564
    • H.R. Dullin, A.V. Ivanov and J.D. Meiss: Normal Forms for Symplectic Maps with Twist Singularities; preprint #2134/564, Loughborough University (2005)
    • (2005) Loughborough University
    • Dullin, H.R.1    Ivanov, A.V.2    Meiss, J.D.3
  • 103
    • 4644273775 scopus 로고    scopus 로고
    • Vanishing twist near focus-focus points
    • p
    • H.R. Dullin and Vũ Ngọc San: Vanishing twist near focus-focus points; Nonlinearity 17, p. 1777–1785 (2004)
    • (2004) Nonlinearity , vol.17 , pp. 1777-1785
    • Dullin, H.R.1    Ngọc San, V.ũ.2
  • 105
    • 2942585296 scopus 로고    scopus 로고
    • Hamiltonian Hopf bifurcation of the hydrogen atom in crossed fields
    • p
    • K. Efstathiou, R.H. Cushman and D.A. Sadovskií: Hamiltonian Hopf bifurcation of the hydrogen atom in crossed fields; Physica D 194, p. 250–274 (2004)
    • (2004) Physica D , vol.194 , pp. 250-274
    • Efstathiou, K.1    Cushman, R.H.2    Sadovskií, D.A.3
  • 106
    • 1642271533 scopus 로고    scopus 로고
    • Perturbations of the 1:1:1 resonance with tetrahedral symmetry: On a three degree of freedom generalization of the two degree of freedom Hénon–Heiles Hamiltonian
    • p
    • K. Efstathiou and D.A. Sadovskií: Perturbations of the 1:1:1 resonance with tetrahedral symmetry: on a three degree of freedom generalization of the two degree of freedom Hénon–Heiles Hamiltonian; Nonlinearity 17, p. 415–446 (2004)
    • (2004) Nonlinearity , vol.17 , pp. 415-446
    • Efstathiou, K.1    Sadovskií, D.A.2
  • 107
    • 1542407759 scopus 로고    scopus 로고
    • Linear Hamiltonian Hopf bifurcation for point-group-invariant perturbations of the 1:1:1 resonance
    • p
    • K. Efstathiou, D.A. Sadovskií and R.H. Cushman: Linear Hamiltonian Hopf bifurcation for point-group-invariant perturbations of the 1:1:1 resonance; Proc. Royal Soc. London 459 #2040, p. 2997–3019 (2003)
    • (2003) Proc. Royal Soc. London , vol.459 , Issue.2040 , pp. 2997-3019
    • Efstathiou, K.1    Sadovskií, D.A.2    Cushman, R.H.3
  • 108
    • 3042561484 scopus 로고    scopus 로고
    • Absolutely Convergent Series Expansions for Quasi Periodic Motions
    • L.H. Eliasson: Absolutely Convergent Series Expansions for Quasi Periodic Motions; Math. Phys. El. J. 2 #4, p. 1–33 (1996)
    • (1996) Math. Phys. El. J. , vol.2 , Issue.4 , pp. 1-33
    • Eliasson, L.H.1
  • 111
    • 21044452798 scopus 로고    scopus 로고
    • Superintegrable Hamiltonian systems: Geometry and Perturbation; p. 93–121 in Symmetry and Perturbation Theory, Cala Gonone 2004 (ed. G. Gaeta)
    • p
    • F. Fassò: Superintegrable Hamiltonian systems: Geometry and Perturbation; p. 93–121 in Symmetry and Perturbation Theory, Cala Gonone 2004 (ed. G. Gaeta) Acta Appl. Math. 87, p. 93-121 (2005)
    • (2005) Acta Appl. Math , vol.87 , pp. 93-121
    • Fassò, F.1
  • 112
    • 0036888081 scopus 로고    scopus 로고
    • Geometric structure of “broadly integrable” Hamiltonian systems
    • p
    • F. Fassò and A. Giacobbe: Geometric structure of “broadly integrable” Hamiltonian systems; J. Geom. Phys. 44, p. 156–170 (2002)
    • (2002) J. Geom. Phys. , vol.44 , pp. 156-170
    • Fassò, F.1    Giacobbe, A.2
  • 114
    • 0037055729 scopus 로고    scopus 로고
    • Quasiperiodic Motions in the Planar Three-Body Problem
    • p
    • J. Féjoz: Quasiperiodic Motions in the Planar Three-Body Problem; J. Diff. Eq. 183, p. 303–341 (2002)
    • (2002) J. Diff. Eq. , vol.183 , pp. 303-341
    • Féjoz, J.1
  • 115
    • 0036041944 scopus 로고    scopus 로고
    • Global secular dynamics in the planar three-body problem
    • p
    • J. Féjoz: Global secular dynamics in the planar three-body problem; Cel. Mech. & Dyn. Astr. 84, p. 159–195 (2002)
    • (2002) Cel. Mech. & Dyn. Astr. , vol.84 , pp. 159-195
    • Féjoz, J.1
  • 116
    • 9444295902 scopus 로고    scopus 로고
    • Démonstration du “théorème d’Arnold” sur la stabilité dusystème planétaire (D’apres M. Herman); Ergod. Th. & Dynam
    • p
    • J. Féjoz: Démonstration du “théorème d’Arnold” sur la stabilité dusystème planétaire (d’apres M. Herman); Ergod. Th. & Dynam. Sys. 24, p. 1521–1582 (2004)
    • (2004) Sys , vol.24 , pp. 1521-1582
    • Féjoz, J.1
  • 117
    • 0008531116 scopus 로고
    • Beweis, daß ein mechanisches Normalsystem im Allgemeinen quasiergodisch ist
    • p
    • E. Fermi: Beweis, daß ein mechanisches Normalsystem im Allgemeinen quasiergodisch ist; Phys. Z. 24, p. 261–265 (1923)
    • (1923) Phys. Z , vol.24 , pp. 261-265
    • Fermi, E.1
  • 118
    • 0005134856 scopus 로고    scopus 로고
    • On perturbed oscillators in 1-1-1 resonance: the case of axially symmetric cubic potentials
    • p
    • S. Ferrer, H. Hanßmann, J. Palacián and P. Yanguas: On perturbed oscillators in 1-1-1 resonance: the case of axially symmetric cubic potentials; J. Geom. Phys. 40, p. 320–369 (2002)
    • (2002) J. Geom. Phys. , vol.40 , pp. 320-369
    • Ferrer, S.1    Hanßmann, H.2    Palacián, J.3    Yanguas, P.4
  • 119
    • 21544483609 scopus 로고
    • Generalized bifurcation of higher-dimensional tori
    • p
    • D. Flockerzi: Generalized bifurcation of higher-dimensional tori; J. Diff. Eq. 55(3), p. 346–367 (1984)
    • (1984) J. Diff. Eq. , vol.55 , Issue.3 , pp. 346-367
    • Flockerzi, D.1
  • 121
    • 0000446018 scopus 로고
    • Twistless KAM tori, quasi flat homoclinic intersections, and other cancellations in the perturbation series of certain completely integrable Hamiltonian systems
    • p
    • G. Gallavotti: Twistless KAM tori, quasi flat homoclinic intersections, and other cancellations in the perturbation series of certain completely integrable Hamiltonian systems. A review; Rev. Math. Phys. 6(3), p. 343–411 (1994)
    • (1994) A Review; Rev. Math. Phys. , vol.6 , Issue.3 , pp. 343-411
    • Gallavotti, G.1
  • 122
    • 0012802473 scopus 로고    scopus 로고
    • Almost invariant elliptic manifold in a singularly perturbed Hamiltonian system
    • p
    • V. Gelfreich and L. Lerman: Almost invariant elliptic manifold in a singularly perturbed Hamiltonian system; Nonlinearity 15, p. 447–457 (2002)
    • (2002) Nonlinearity , vol.15 , pp. 447-457
    • Gelfreich, V.1    Lerman, L.2
  • 124
    • 0001859493 scopus 로고
    • Rigorous estimates for the series expansions of Hamiltonian perturbation theory
    • p
    • A. Giorgilli and L. Galvani: Rigorous estimates for the series expansions of Hamiltonian perturbation theory; Celest. Mech. 37, p. 95–112 (1985)
    • (1985) Celest. Mech. , vol.37 , pp. 95-112
    • Giorgilli, A.1    Galvani, L.2
  • 125
    • 0000163515 scopus 로고
    • Effective Stability for a Hamiltonian System near an Elliptic Equilibrium Point, with an Application to the Restricted Three Body Problem
    • p
    • A. Giorgilli, A. Delshams, E. Fontich, L. Galvani and C. Simó: Effective Stability for a Hamiltonian System near an Elliptic Equilibrium Point, with an Application to the Restricted Three Body Problem; J. Diff. Eq. 77, p. 167–198 (1989)
    • (1989) J. Diff. Eq. , vol.77 , pp. 167-198
    • Giorgilli, A.1    Delshams, A.2    Fontich, E.3    Galvani, L.4    Simó, C.5
  • 127
    • 85072819671 scopus 로고
    • The Constrained Liapunov–Schmidt Procedure and Periodic Orbits; p. 81–127 in Normal Forms and Homoclinic Chaos, Waterloo 1992 (eds. W.F. Langford and W
    • M. Golubitsky, J.E. Marsden, I. Stewart and M. Dellnitz: The Constrained Liapunov–Schmidt Procedure and Periodic Orbits; p. 81–127 in Normal Forms and Homoclinic Chaos, Waterloo 1992 (eds. W.F. Langford and W. Nagata) Fields Institute Communications 4 AMS (1995)
    • (1995) Nagata) Fields Institute Communications 4 AMS
    • Golubitsky, M.1    Marsden, J.E.2    Stewart, I.3    Dellnitz, M.4
  • 128
    • 0001454797 scopus 로고
    • Generic bifurcation of Hamiltonian systems with symmetry
    • p
    • M. Golubitsky and I. Stewart: Generic bifurcation of Hamiltonian systems with symmetry; Physica D 24, p. 391–405 (1987)
    • (1987) Physica D , vol.24 , pp. 391-405
    • Golubitsky, M.1    Stewart, I.2
  • 130
    • 25144442314 scopus 로고    scopus 로고
    • A universal procedure for normalizing n-degree-of-freedom polynomial Hamiltonian systems
    • p
    • S. Gutiérrez-Romero, J.F. Palacián and P. Yanguas: A universal procedure for normalizing n-degree-of-freedom polynomial Hamiltonian systems; SIAM J. Math. Anal. 65(4), p. 1130–1152 (2005)
    • (2005) SIAM J. Math. Anal. , vol.65 , Issue.4 , pp. 1130-1152
    • Gutiérrez-Romero, S.1    Palacián, J.F.2    Yanguas, P.3
  • 131
    • 85072831851 scopus 로고
    • Whiskered tori and chaos in resonant Hamiltonian normal forms; p. 129–149 in Normal Forms and Homoclinic Chaos, Waterloo 1992 (eds. W.F. Langford and W
    • G. Haller and S. Wiggins: Whiskered tori and chaos in resonant Hamiltonian normal forms; p. 129–149 in Normal Forms and Homoclinic Chaos, Waterloo 1992 (eds. W.F. Langford and W. Nagata) Fields Institute Communications 4 AMS (1995)
    • (1995) Nagata) Fields Institute Communications 4 AMS
    • Haller, G.1    Wiggins, S.2
  • 132
    • 0000318075 scopus 로고    scopus 로고
    • Geometry and chaos near resonant equilibria of 3-DOF Hamiltonian systems
    • p
    • G. Haller and S. Wiggins: Geometry and chaos near resonant equilibria of 3-DOF Hamiltonian systems; Physica D 90, p. 319–365 (1996)
    • (1996) Physica D , vol.90 , pp. 319-365
    • Haller, G.1    Wiggins, S.2
  • 134
    • 85072831281 scopus 로고    scopus 로고
    • p. 151–173 in Normal Forms and Homoclinic Chaos, Waterloo 1992 (eds. W.F. Langford and W. Nagata) Fields Institute Communications 4 AMS (1995)
    • H. Hanßmann: Normal Forms for Perturbations of the Euler Top; p. 151–173 in Normal Forms and Homoclinic Chaos, Waterloo 1992 (eds. W.F. Langford and W. Nagata) Fields Institute Communications 4 AMS (1995)
    • Normal Forms for Perturbations of the Euler Top
    • Hanßmann, H.1
  • 136
    • 85072841040 scopus 로고
    • Equivariant Perturbations of the Euler Top; p. 227–253 in Nonlinear Dynamical Systems and Chaos
    • (eds. H.W. Broer et al.) Birkhäuser (1996)
    • H. Hanßmann: Equivariant Perturbations of the Euler Top; p. 227–253 in Nonlinear Dynamical Systems and Chaos, Groningen 1995 (eds. H.W. Broer et al.) Birkhäuser (1996)
    • (1995) Groningen
    • Hanßmann, H.1
  • 137
    • 4243518566 scopus 로고    scopus 로고
    • Quasi-periodic Motions of a Rigid Body I – Quadratic Hamiltonians on the Sphere with a Distinguished Parameter
    • p
    • H. Hanßmann: Quasi-periodic Motions of a Rigid Body I – Quadratic Hamiltonians on the Sphere with a Distinguished Parameter; Reg. & Chaot. Dyn. 2(2), p. 41–57 (1997)
    • (1997) Reg. & Chaot. Dyn. , vol.2 , Issue.2 , pp. 41-57
    • Hanßmann, H.1
  • 138
    • 4243911013 scopus 로고    scopus 로고
    • The reversible umbilic bifurcation; p. 81–94 in Time-reversal symmetry in dynamical systems, Warwick 1996 (ed. J.S.W. Lamb)
    • H. Hanßmann: The reversible umbilic bifurcation; p. 81–94 in Time-reversal symmetry in dynamical systems, Warwick 1996 (ed. J.S.W. Lamb), Physica D 112 (1998)
    • (1998) Physica D , vol.112
    • Hanßmann, H.1
  • 139
    • 0010138127 scopus 로고    scopus 로고
    • The Quasi-Periodic Centre-Saddle Bifurcation
    • p
    • H. Hanßmann: The Quasi-Periodic Centre-Saddle Bifurcation; J. Diff. Eq. 142(2), p. 305–370 (1998)
    • (1998) J. Diff. Eq. , vol.142 , Issue.2 , pp. 305-370
    • Hanßmann, H.1
  • 140
    • 85072840339 scopus 로고    scopus 로고
    • in New Advances in Celestial Mechanics and Hamiltonian systems, Guanajuato 2001 (eds. J. Delgado et al.) Kluwer/Plenum (2004)
    • H. Hanßmann: A Survey on Bifurcations of Invariant Tori; p. 109–121 in New Advances in Celestial Mechanics and Hamiltonian systems, Guanajuato 2001 (eds. J. Delgado et al.) Kluwer/Plenum (2004)
    • A Survey on Bifurcations of Invariant Tori , pp. 109-121
    • Hanßmann, H.1
  • 141
    • 29244474361 scopus 로고    scopus 로고
    • in Dynamic Systems and Applications, Atlanta 2003 (eds. G.S. Ladde, N.G. Medhin and M. Sambandham) Dynamic Publishers (2004)
    • H. Hanßmann: Hamiltonian Torus Bifurcations Related to Simple Singularities; p. 679–685 in Dynamic Systems and Applications, Atlanta 2003 (eds. G.S. Ladde, N.G. Medhin and M. Sambandham) Dynamic Publishers (2004)
    • Hamiltonian Torus Bifurcations Related to Simple Singularities , pp. 679-685
    • Hanßmann, H.1
  • 143
    • 85072836598 scopus 로고    scopus 로고
    • Fifth Euromech Nonlinear Dynamics Conference, Eindhoven 2005 (eds. D.H. van Campen, M.D. Lazurko and W.P.J.M. van den Oever) Technische Universiteit Eindhoven (2005)
    • H. Hanßmann: Perturbations of integrable and superintegrable Hamiltonian systems; p. 1527–1536 in Fifth Euromech Nonlinear Dynamics Conference, Eindhoven 2005 (eds. D.H. van Campen, M.D. Lazurko and W.P.J.M. van den Oever) Technische Universiteit Eindhoven (2005)
    • Perturbations of Integrable and Superintegrable Hamiltonian Systems , pp. 1527-1536
    • Hanßmann, H.1
  • 144
    • 33744967972 scopus 로고    scopus 로고
    • On Hamiltonian bifurcations of invariant tori with a Floquet multiplier −1
    • p
    • H. Hanßmann: On Hamiltonian bifurcations of invariant tori with a Floquet multiplier −1; Dynamical Systems 21(2), p. 115–145 (2006)
    • (2006) Dynamical Systems , vol.21 , Issue.2 , pp. 115-145
    • Hanßmann, H.1
  • 146
    • 1542561309 scopus 로고    scopus 로고
    • On the Hamiltonian Hopf bifurcations in the 3D Hénon–Heiles family
    • p
    • H. Hanßmann and J.C. van der Meer: On the Hamiltonian Hopf bifurcations in the 3D Hénon–Heiles family; J. Dynamics Diff. Eq. 14, p. 675–695 (2002)
    • (2002) J. Dynamics Diff. Eq. , vol.14 , pp. 675-695
    • Hanßmann, H.1    van der Meer, J.C.2
  • 148
    • 24344485078 scopus 로고    scopus 로고
    • Algebraic methods for determining Hamiltonian Hopf bifurcations in three-degree-of-freedom systems
    • p
    • H. Hanßmann and J.C. van der Meer: Algebraic methods for determining Hamiltonian Hopf bifurcations in three-degree-of-freedom systems; J. Dynamics Diff. Eq. 17(3), p. 453–474 (2005)
    • (2005) J. Dynamics Diff. Eq. , vol.17 , Issue.3 , pp. 453-474
    • Hanßmann, H.1    van der Meer, J.C.2
  • 149
    • 18044404153 scopus 로고    scopus 로고
    • A degenerate bifurcation in the Hénon–Heiles family
    • p
    • H. Hanßmann and B. Sommer: A degenerate bifurcation in the Hénon–Heiles family; Cel. Mech. & Dyn. Astr. 81(3), p. 249–261 (2001)
    • (2001) Cel. Mech. & Dyn. Astr. , vol.81 , Issue.3 , pp. 249-261
    • Hanßmann, H.1    Sommer, B.2
  • 150
    • 0006716250 scopus 로고
    • Bifurcation at complex instability
    • p
    • D.C. Heggie: Bifurcation at complex instability; Cel. Mech. 35, p. 357–382 (1985)
    • (1985) Cel. Mech. , vol.35 , pp. 357-382
    • Heggie, D.C.1
  • 152
    • 0038613885 scopus 로고    scopus 로고
    • Stepwise precession of the resonant swinging spring
    • p
    • D.D. Holm and P. Lynch: Stepwise precession of the resonant swinging spring; SIAM J. Appl. Dynam. Syst. 1, p. 44–64 (2002)
    • (2002) SIAM J. Appl. Dynam. Syst. , vol.1 , pp. 44-64
    • Holm, D.D.1    Lynch, P.2
  • 154
    • 84980080650 scopus 로고
    • A Mathematical Example Displaying Features of Turbulence
    • p
    • E. Hopf: A Mathematical Example Displaying Features of Turbulence; Comm. (Pure) Appl. Math. 1, p. 303–322 (1948)
    • (1948) Comm. (Pure) Appl. Math. , vol.1 , pp. 303-322
    • Hopf, E.1
  • 155
    • 85072844818 scopus 로고
    • Repeated branching through loss of stability, an example; p. 49–56 in Proceedings of the conference on differential equations, Maryland 1955 (ed. J.B. Diaz) Univ
    • E. Hopf: Repeated branching through loss of stability, an example; p. 49–56 in Proceedings of the conference on differential equations, Maryland 1955 (ed. J.B. Diaz) Univ. Maryland book store (1956)
    • (1956) Maryland Book Store
    • Hopf, E.1
  • 157
    • 0030577964 scopus 로고    scopus 로고
    • Versal Deformations and Normal Forms for Reversible and Hamiltonian Linear Systems
    • p
    • I. Hoveijn: Versal Deformations and Normal Forms for Reversible and Hamiltonian Linear Systems; J. Diff. Eq. 126(2), p. 408–442 (1996)
    • (1996) J. Diff. Eq. , vol.126 , Issue.2 , pp. 408-442
    • Hoveijn, I.1
  • 158
    • 0002025569 scopus 로고
    • Chaos in the 1:2:3 Hamiltonian normal form
    • p
    • I. Hoveijn and F. Verhulst: Chaos in the 1:2:3 Hamiltonian normal form; Physica D 44(3), p. 397–406 (1990)
    • (1990) Physica D , vol.44 , Issue.3 , pp. 397-406
    • Hoveijn, I.1    Verhulst, F.2
  • 160
    • 0033631985 scopus 로고    scopus 로고
    • On the persistence of lower-dimensional invariant hyperbolic tori for smooth Hamiltonian systems
    • p
    • D. Huang and Z. Liu: On the persistence of lower-dimensional invariant hyperbolic tori for smooth Hamiltonian systems; Nonlinearity 13(1), p. 189– 202 (2000)
    • (2000) Nonlinearity , vol.13 , Issue.1 , pp. 189-202
    • Huang, D.1    Liu, Z.2
  • 161
    • 0142146148 scopus 로고    scopus 로고
    • Quasiperiodic breathers in systems of weakly coupled pendulums
    • Ph.D. Thesis
    • H.H. de Jong: Quasiperiodic breathers in systems of weakly coupled pendulums; Ph.D. Thesis, Rijksuniversiteit Groningen (1999)
    • (1999) Rijksuniversiteit Groningen
    • de Jong, H.H.1
  • 162
    • 85072834668 scopus 로고    scopus 로고
    • in Hamiltonian Systems with Three or More Degrees of Freedom, S’Agaró 1995 (ed. C. Simó) NATO Adv. Sci. Inst. C 533, Kluwer (1999)
    • À. Jorba, R. de la Llave and M. Zou: Lindstedt series for lower dimensional tori; p. 151–167 in Hamiltonian Systems with Three or More Degrees of Freedom, S’Agaró 1995 (ed. C. Simó) NATO Adv. Sci. Inst. C 533, Kluwer (1999)
    • Lindstedt Series for Lower Dimensional Tori , pp. 151-167
    • Jorba, À.1    de la Llave, R.2    Zou, M.3
  • 163
    • 0000500437 scopus 로고    scopus 로고
    • On the persistence of lower dimensional invariant tori under quasi-periodic perturbations
    • p
    • À. Jorba and J. Villanueva: On the persistence of lower dimensional invariant tori under quasi-periodic perturbations, J. Nonlinear Sci. 7, p. 427–473 (1997)
    • (1997) J. Nonlinear Sci. , vol.7 , pp. 427-473
    • Jorba, À.1    Villanueva, J.2
  • 164
    • 0040507795 scopus 로고    scopus 로고
    • On the normal behaviour of partially elliptic lower-dimensional tori of Hamiltonian systems
    • p
    • À. Jorba and J. Villanueva: On the normal behaviour of partially elliptic lower-dimensional tori of Hamiltonian systems; Nonlinearity 10, p. 783–822 (1997)
    • (1997) Nonlinearity , vol.10 , pp. 783-822
    • Jorba, À.1    Villanueva, J.2
  • 165
    • 0000738308 scopus 로고
    • Normal Forms and Versal Deformations of Linear Hamiltonian Systems; J
    • p
    • H. Koçak: Normal Forms and Versal Deformations of Linear Hamiltonian Systems; J. Diff. Eq. 51, p. 353–407 (1984)
    • (1984) Diff. Eq. , vol.51 , pp. 353-407
    • Koçak, H.1
  • 166
    • 85072830478 scopus 로고
    • O sohranenii uslovno-periodiqeskih dviжeniĭ pri malom izmenenii funkcii Gamilbtona
    • Dokl. akad. nauk SSSR 98, p. 527–530 (1954) – translated as: Preservation of conditionally periodic movements with small change in the Hamilton function; p. 51–56 in Stochastic Behavior in Classical and Quantum Hamiltonian Systems, Como 1977 (eds. G. Casati and J. Ford) Lect. Notes Phys. 93, Springer (1979) – reprinted p. 81–86 in Chaos (ed. Bai Lin Hao) World Scientifi
    • A.N. Kolmogorov: O sohranenii uslovno-periodiqeskih dviжeniĭ pri malom izmenenii funkcii Gamilbtona; Dokl. akad. nauk SSSR 98, p. 527–530 (1954) – translated as: Preservation of conditionally periodic movements with small change in the Hamilton function; p. 51–56 in Stochastic Behavior in Classical and Quantum Hamiltonian Systems, Como 1977 (eds. G. Casati and J. Ford) Lect. Notes Phys. 93, Springer (1979) – reprinted p. 81–86 in Chaos (ed. Bai Lin Hao) World Scientific (1984)
    • (1984) Lect. Notes Phys
    • Kolmogorov, A.N.1
  • 167
    • 0033099426 scopus 로고    scopus 로고
    • Réductibilité presque partout des flots fibrés quasi-périodiques à valeurs dans des groupes compactes
    • p
    • R. Krikorian: Réductibilité presque partout des flots fibrés quasi-périodiques à valeurs dans des groupes compactes; Ann. Sci. École Norm. Sup. 4 32(2), p. 187–240 (1999)
    • (1999) Ann. Sci. École Norm. Sup. 4 , vol.32 , Issue.2 , pp. 187-240
    • Krikorian, R.1
  • 169
    • 0002036330 scopus 로고
    • On Resonant Nonlinearly Coupled Oscillators with Two Equal Frequencies
    • p
    • M. Kummer: On Resonant Nonlinearly Coupled Oscillators with Two Equal Frequencies; Comm. Math. Phys. 48, p. 53–79 (1976)
    • (1976) Comm. Math. Phys. , vol.48 , pp. 53-79
    • Kummer, M.1
  • 170
    • 0002008510 scopus 로고
    • On Resonant Classical Hamiltonians with Two Equal Frequencies
    • p
    • M. Kummer: On Resonant Classical Hamiltonians with Two Equal Frequencies; Comm. Math. Phys. 58, p. 85–112 (1978)
    • (1978) Comm. Math. Phys. , vol.58 , pp. 85-112
    • Kummer, M.1
  • 171
    • 85072832142 scopus 로고    scopus 로고
    • in Local and global methods of nonlinear dynamics, Silver Spring 1984 (eds. A.V. Sáenz, W.W. Zachary and R. Cawley) Lect. Notes Phys. 252, Springer (1986)
    • M. Kummer: On resonant Hamiltonian systems with finitely many degrees of freedom; p. 19–31 in Local and global methods of nonlinear dynamics, Silver Spring 1984 (eds. A.V. Sáenz, W.W. Zachary and R. Cawley) Lect. Notes Phys. 252, Springer (1986)
    • On Resonant Hamiltonian Systems with Finitely Many Degrees of Freedom , pp. 19-31
    • Kummer, M.1
  • 172
    • 38249019449 scopus 로고
    • On Resonant Classical Hamiltonians with n Frequencies
    • p
    • M. Kummer: On Resonant Classical Hamiltonians with n Frequencies; J. Diff. Eq. 83, p. 220–243 (1990)
    • (1990) J. Diff. Eq. , vol.83 , pp. 220-243
    • Kummer, M.1
  • 174
    • 0036489720 scopus 로고    scopus 로고
    • Perturbed ion traps: A generalization of the three-dimensional Hénon–Heiles problem
    • p
    • V. Lanchares, A.I. Pascual, J. Palacián, P. Yanguas and J.P. Salas: Perturbed ion traps: A generalization of the three-dimensional Hénon–Heiles problem; Chaos 12(1), p. 87–99 (2002)
    • (2002) Chaos , vol.12 , Issue.1 , pp. 87-99
    • Lanchares, V.1    Pascual, A.I.2    Palacián, J.3    Yanguas, P.4    Salas, J.P.5
  • 175
    • 0036687711 scopus 로고    scopus 로고
    • Persistence of invariant tori in generalized Hamiltonian systems
    • p
    • Y. Li and Y. Yi: Persistence of invariant tori in generalized Hamiltonian systems; Ergod. Th. & Dynam. Syst. 22(4), p. 1233–1261 (2002)
    • (2002) Ergod. Th. & Dynam. Syst. , vol.22 , Issue.4 , pp. 1233-1261
    • Li, Y.1    Yi, Y.2
  • 176
    • 0000763991 scopus 로고
    • Existence of Quasi-Periodic Solutions to the Three-Body Problem
    • p
    • B.B. Lieberman: Existence of Quasi-Periodic Solutions to the Three-Body Problem; Celest. Mech. 3, p. 408–426 (1971)
    • (1971) Celest. Mech. , vol.3 , pp. 408-426
    • Lieberman, B.B.1
  • 177
    • 0039985132 scopus 로고
    • Quasi-Periodic Solutions of Hamiltonian Systems
    • p
    • B.B. Lieberman: Quasi-Periodic Solutions of Hamiltonian Systems; J. Diff. Eq. 11, p. 109–137 (1972)
    • (1972) J. Diff. Eq. , vol.11 , pp. 109-137
    • Lieberman, B.B.1
  • 179
    • 85072822577 scopus 로고    scopus 로고
    • Equadiff 2003, Hasselt 2003 (eds. F. Dumortier et al.) World Scientific (2005)
    • A. Litvak-Hinenzon: The mechanism of parabolic resonance orbits; p. 738– 743 in: Equadiff 2003, Hasselt 2003 (eds. F. Dumortier et al.) World Scientific (2005)
    • The Mechanism of Parabolic Resonance Orbits , pp. 738-743
    • Litvak-Hinenzon, A.1
  • 181
    • 0037089436 scopus 로고    scopus 로고
    • Parabolic resonances in 3 degree of freedom near-integrable Hamiltonian systems
    • p
    • A. Litvak-Hinenzon and V. Rom-Kedar: Parabolic resonances in 3 degree of freedom near-integrable Hamiltonian systems; Physica D 164, p. 213–250 (2002)
    • (2002) Physica D , vol.164 , pp. 213-250
    • Litvak-Hinenzon, A.1    Rom-Kedar, V.2
  • 182
    • 0042384685 scopus 로고    scopus 로고
    • Resonant tori and instabilities in Hamiltonian systems
    • p
    • A. Litvak-Hinenzon and V. Rom-Kedar: Resonant tori and instabilities in Hamiltonian systems; Nonlinearity 15, p. 1149–1177 (2002)
    • (2002) Nonlinearity , vol.15 , pp. 1149-1177
    • Litvak-Hinenzon, A.1    Rom-Kedar, V.2
  • 184
    • 0002990093 scopus 로고
    • On Quadratic Poisson Structures
    • p
    • Z.-J. Liu and P. Xu: On Quadratic Poisson Structures; Lett. Math. Phys. 26, p. 33–42 (1992)
    • (1992) Lett. Math. Phys. , vol.26 , pp. 33-42
    • Liu, Z.-J.1    Xu, P.2
  • 186
    • 77957172363 scopus 로고
    • Dédoublement de courbes invariantes sur le cylindre: Petit diviseurs
    • p
    • J. Los: Dédoublement de courbes invariantes sur le cylindre: petit diviseurs; Ann. Inst. H. Poincaré, Analyse non linéaire 5(1), p. 37–95 (1988)
    • (1988) Ann. Inst. H. Poincaré, Analyse Non linéaire , vol.5 , Issue.1 , pp. 37-95
    • Los, J.1
  • 187
    • 0347550173 scopus 로고
    • 3 and doubling bifurcation
    • p
    • 3 and doubling bifurcation; Nonlinearity 2, p. 149–174 (1989)
    • (1989) Nonlinearity , vol.2 , pp. 149-174
    • Los, J.1
  • 190
    • 4744369139 scopus 로고    scopus 로고
    • Stability and instability for Gevrey quasi-convex near-integrable Hamiltonian systems
    • p
    • J.-P. Marco and D. Sauzin: Stability and instability for Gevrey quasi-convex near-integrable Hamiltonian systems; Publ. Math., Inst. Hautes Etud. Sci. 96, p. 199–275 (2003)
    • (2003) Publ. Math., Inst. Hautes Etud. Sci. , vol.96 , pp. 199-275
    • Marco, J.-P.1    Sauzin, D.2
  • 192
    • 0002015290 scopus 로고
    • Periodic orbits and solenoids in generic Hamiltonian dynamical systems
    • p
    • L. Markus and K.R. Meyer: Periodic orbits and solenoids in generic Hamiltonian dynamical systems; Am. J. Math. 102(1), p. 25–92 (1980)
    • (1980) Am. J. Math. , vol.102 , Issue.1 , pp. 25-92
    • Markus, L.1    Meyer, K.R.2
  • 194
    • 49549151837 scopus 로고
    • Reduction of symplectic manifolds with symmetry
    • p
    • J.E. Marsden and A. Weinstein: Reduction of symplectic manifolds with symmetry; Rep. Math. Phys. 5(1), p. 121–130 (1974)
    • (1974) Rep. Math. Phys. , vol.5 , Issue.1 , pp. 121-130
    • Marsden, J.E.1    Weinstein, A.2
  • 195
    • 3342914757 scopus 로고    scopus 로고
    • Practical normal form computations for vector fields
    • p
    • S. Mayer, J. Scheurle and S. Walcher: Practical normal form computations for vector fields; Z. angew. Math. Mech. 84(7), p. 472–482 (2004)
    • (2004) Z. Angew. Math. Mech. , vol.84 , Issue.7 , pp. 472-482
    • Mayer, S.1    Scheurle, J.2    Walcher, S.3
  • 196
    • 0031522248 scopus 로고    scopus 로고
    • KAM theorem for generic analytic perturbations of the Euler system
    • p
    • M. Mazzocco: KAM theorem for generic analytic perturbations of the Euler system; Z. Angew. Math. Phys. 48, p. 193–219 (1997)
    • (1997) Z. Angew. Math. Phys. , vol.48 , pp. 193-219
    • Mazzocco, M.1
  • 197
    • 0002340069 scopus 로고
    • Nonsemisimple 1:1 resonance at an equilibrium
    • p
    • J.C. van der Meer: Nonsemisimple 1:1 resonance at an equilibrium; Celest. Mech. 27, p. 131–149 (1982)
    • (1982) Celest. Mech. , vol.27 , pp. 131-149
    • van der Meer, J.C.1
  • 199
    • 0001203818 scopus 로고
    • Hamiltonian Hopf bifurcation with symmetry
    • p
    • J.C. van der Meer: Hamiltonian Hopf bifurcation with symmetry; Nonlinearity 3, p. 1041–1056 (1990)
    • (1990) Nonlinearity , vol.3 , pp. 1041-1056
    • Meer, J.C.1
  • 200
    • 85072818871 scopus 로고    scopus 로고
    • Conservative systems and quantum chaos, Waterloo 1992; (eds. L.M. Bates and D.L. Rod) Fields Institute Communications 8 AMS (1996)
    • J.C. van der Meer: Degenerate Hamiltonian Hopf bifurcations; p. 159–176 in Conservative systems and quantum chaos, Waterloo 1992; (eds. L.M. Bates and D.L. Rod) Fields Institute Communications 8 AMS (1996)
    • Degenerate Hamiltonian Hopf Bifurcations , pp. 159-176
    • van der Meer, J.C.1
  • 201
    • 0038977610 scopus 로고
    • Constrained normalization of Hamiltonian systems and perturbed Keplerian motion
    • p
    • J.C. van der Meer and R. Cushman: Constrained normalization of Hamiltonian systems and perturbed Keplerian motion; Z. Angew. Math. Phys. 37(3), p. 402–424 (1986)
    • (1986) Z. Angew. Math. Phys. , vol.37 , Issue.3 , pp. 402-424
    • van der Meer, J.C.1    Cushman, R.2
  • 202
    • 85072846730 scopus 로고
    • Orbiting dust under radiation pressure; p. 403–414 in Differential Geometric Methods in Theoretical Physics, Clausthal, 1986 (ed. H
    • J.C. van der Meer and R. Cushman: Orbiting dust under radiation pressure; p. 403–414 in Differential Geometric Methods in Theoretical Physics, Clausthal, 1986 (ed. H. Doebner) World Scientific (1987)
    • (1987) Doebner) World Scientific
    • van der Meer, J.C.1    Cushman, R.2
  • 203
    • 0001229841 scopus 로고
    • Class renormalization: Islands around islands
    • p
    • J.D. Meiss: Class renormalization: Islands around islands; Phys. Rev. A 34(3), p. 2375–2383 (1986)
    • (1986) Phys. Rev. A , vol.34 , Issue.3 , pp. 2375-2383
    • Meiss, J.D.1
  • 204
    • 0001020164 scopus 로고
    • On some cases of conservation of conditionally periodic motions under a small change of the Hamiltonian function
    • p
    • V.K. Mel’nikov: On some cases of conservation of conditionally periodic motions under a small change of the Hamiltonian function; Sov. Math. Dokl. 6(6), p. 1592–1596 (1965)
    • (1965) Sov. Math. Dokl. , vol.6 , Issue.6 , pp. 1592-1596
    • Mel’Nikov, V.K.1
  • 205
    • 84966219641 scopus 로고
    • Generic bifurcation of periodic points
    • p
    • K.R. Meyer: Generic bifurcation of periodic points; Trans. AMS 149, p. 95–107 (1970)
    • (1970) Trans. AMS , vol.149 , pp. 95-107
    • Meyer, K.R.1
  • 206
    • 0002681954 scopus 로고    scopus 로고
    • p. 259–272 in Dynamical Systems (ed. M.M. Peixoto), Academic Press (1973)
    • K.R. Meyer: Symmetries and integrals in mathematics; p. 259–272 in Dynamical Systems (ed. M.M. Peixoto), Academic Press (1973)
    • Symmetries and Integrals in Mathematics
    • Meyer, K.R.1
  • 207
    • 0001865471 scopus 로고    scopus 로고
    • Dynamical Systems — Warwick 1974 (ed. A. Manning) LNM 468, Springer (1975)
    • K.R. Meyer: Generic Bifurcation in Hamiltonian Systems; p. 62–70 in Dynamical Systems — Warwick 1974 (ed. A. Manning) LNM 468, Springer (1975)
    • Generic Bifurcation in Hamiltonian Systems , pp. 62-70
    • Meyer, K.R.1
  • 209
    • 0001410062 scopus 로고
    • The stability of the Lagrange triangular point andatheoremofArnold
    • p
    • K.R. Meyer and D.S. Schmidt: The stability of the Lagrange triangular point andatheoremofArnold;J. Diff. Eq. 62(2), p. 222–236 (1986)
    • (1986) J. Diff. Eq. , vol.62 , Issue.2 , pp. 222-236
    • Meyer, K.R.1    Schmidt, D.S.2
  • 210
    • 84966208299 scopus 로고
    • Melnikov Transforms, Bernoulli Bundles, and Almost Periodic Perturbations
    • p
    • K.R. Meyer and G.R. Sell: Melnikov Transforms, Bernoulli Bundles, and Almost Periodic Perturbations; Trans. AMS 314(1), p. 63–105 (1989)
    • (1989) Trans. AMS , vol.314 , Issue.1 , pp. 63-105
    • Meyer, K.R.1    Sell, G.R.2
  • 212
    • 0002023955 scopus 로고
    • Generalized Liouville method of integration of Hamiltonian systems
    • p
    • A.S. Mishchenko and A.T. Fomenko: Generalized Liouville method of integration of Hamiltonian systems; Funct. Anal. Appl. 12(2), p. 113–121 (1978)
    • (1978) Funct. Anal. Appl. , vol.12 , Issue.2 , pp. 113-121
    • Mishchenko, A.S.1    Fomenko, A.T.2
  • 213
    • 34249759431 scopus 로고
    • Superexponential Stability of KAM Tori
    • p
    • A. Morbidelli and A. Giorgilli: Superexponential Stability of KAM Tori; J. Stat. Phys. 78(5/6), p. 1607–1617 (1995)
    • (1995) J. Stat. Phys. , vol.78 , Issue.5-6 , pp. 1607-1617
    • Morbidelli, A.1    Giorgilli, A.2
  • 214
    • 0001713329 scopus 로고
    • On a connection between KAM and Nekhoroshev’s theorems
    • p
    • A. Morbidelli and A. Giorgilli: On a connection between KAM and Nekhoroshev’s theorems; Physica D 86(3), p. 514–516 (1995)
    • (1995) Physica D , vol.86 , Issue.3 , pp. 514-516
    • Morbidelli, A.1    Giorgilli, A.2
  • 215
    • 0001851184 scopus 로고
    • On Invariant Curves of Area-Preserving Mappings of an Annulus
    • J. Moser: On Invariant Curves of Area-Preserving Mappings of an Annulus; Nachr. Akad. Wiss. Göttingen, II. Math.-Phys. Kl. 1962(1), p. 1–20 (1962)
    • (1962) Nachr. Akad. Wiss. Göttingen, II. Math.-Phys. Kl. , vol.1962 , Issue.1 , pp. 1-20
    • Moser, J.1
  • 216
    • 3042570326 scopus 로고
    • Convergent Series Expansion for Quasi-Periodic Motions
    • p
    • J. Moser: Convergent Series Expansion for Quasi-Periodic Motions; Math. Ann. 169(1), p. 136–176 (1967)
    • (1967) Math. Ann. , vol.169 , Issue.1 , pp. 136-176
    • Moser, J.1
  • 217
    • 84980140116 scopus 로고
    • Periodic Orbits near an Equilibrium and a Theorem by Alan Weinstein
    • p
    • J. Moser: Periodic Orbits near an Equilibrium and a Theorem by Alan Weinstein; Comm. Pure Appl. Math. 29, p. 727–747 (1976)
    • (1976) Comm. Pure Appl. Math. , vol.29 , pp. 727-747
    • Moser, J.1
  • 219
    • 0000234399 scopus 로고
    • Action-angle variables and their generalizations
    • p
    • N.N. Nekhoroshev: Action-angle variables and their generalizations; Trans. Mosc. Math. Soc. 26, p. 180–198 (1972)
    • (1972) Trans. Mosc. Math. Soc. , vol.26 , pp. 180-198
    • Nekhoroshev, N.N.1
  • 220
    • 84908024292 scopus 로고
    • An exponential estimate of the time of stability of nearlyintegrable Hamiltonian systems
    • p
    • N.N. Nekhoroshev: An exponential estimate of the time of stability of nearlyintegrable Hamiltonian systems; Russ. Math. Surv. 32(6), p. 1–65 (1977)
    • (1977) Russ. Math. Surv. , vol.32 , Issue.6 , pp. 1-65
    • Nekhoroshev, N.N.1
  • 222
    • 49049145278 scopus 로고
    • Estimates in the Kolmogorov theorem on conservation of conditionally periodic motions
    • p
    • A.I. Neishtadt: Estimates in the Kolmogorov theorem on conservation of conditionally periodic motions; J. Appl. Math. Mech. 45, p. 766–772 (1982)
    • (1982) J. Appl. Math. Mech , vol.45 , pp. 766-772
    • Neishtadt, A.I.1
  • 224
    • 0041581444 scopus 로고    scopus 로고
    • Kolmogorov condition for integrable systems with focusfocus singularities
    • p
    • Nguyen Tien Zung: Kolmogorov condition for integrable systems with focusfocus singularities; Phys. Lett. A 215, p. 40–44 (1996)
    • (1996) Phys. Lett. A , vol.215 , pp. 40-44
    • Zung, N.T.1
  • 225
    • 9344225119 scopus 로고    scopus 로고
    • A note on focus-focus singularities
    • p
    • Nguyen Tien Zung: A note on focus-focus singularities; Diff. Geom. Appl. 7(2), p. 123–130 (1997)
    • (1997) Diff. Geom. Appl. , vol.7 , Issue.2 , pp. 123-130
    • Zung, N.T.1
  • 228
    • 23844497722 scopus 로고    scopus 로고
    • Dynamics close to a non semi-simple 1:−1 resonance periodic orbit
    • p
    • M. Ollé, J.R. Pacha and J. Villanueva: Dynamics close to a non semi-simple 1:−1 resonance periodic orbit; Discr. Cont. Dyn. Syst. B 5, p. 799–816 (2005)
    • (2005) Discr. Cont. Dyn. Syst. B , vol.5 , pp. 799-816
    • Ollé, M.1    Pacha, J.R.2    Villanueva, J.3
  • 229
    • 23844508917 scopus 로고    scopus 로고
    • Quantitative estimates on the normal form around a non-semi-simple 1:−1 resonant periodic orbit
    • p
    • M. Ollé, J.R. Pacha and J. Villanueva: Quantitative estimates on the normal form around a non-semi-simple 1:−1 resonant periodic orbit; Nonlinearity 18, p. 1141–1172 (2005)
    • (2005) Nonlinearity , vol.18 , pp. 1141-1172
    • Ollé, M.1    Pacha, J.R.2    Villanueva, J.3
  • 230
    • 85072834562 scopus 로고    scopus 로고
    • Momentum Maps and Hamiltonian Reduction; Progress in Mathematics 222
    • J.-P. Ortega and T.S. Raţiu: Momentum Maps and Hamiltonian Reduction; Progress in Mathematics 222, Birkhäuser (2004)
    • (2004) Birkhäuser
    • Ortega, J.-P.1    Raţiu, T.S.2
  • 233
    • 0034216023 scopus 로고    scopus 로고
    • Reduction of polynomial Hamiltonians by the construction of formal integrals
    • p
    • J. Palacián and P. Yanguas: Reduction of polynomial Hamiltonians by the construction of formal integrals; Nonlinearity 13, p. 1021–1054 (2000)
    • (2000) Nonlinearity , vol.13 , pp. 1021-1054
    • Palacián, J.1    Yanguas, P.2
  • 235
    • 12444261812 scopus 로고    scopus 로고
    • Stability of Poisson Equilibria and Hamiltonian Relative Equilibria by Energy Methods
    • p
    • G.W. Patrick, M. Roberts and C. Wulff: Stability of Poisson Equilibria and Hamiltonian Relative Equilibria by Energy Methods; Arch. Rat. Mech. An. 173(3), p. 301–344 (2004)
    • (2004) Arch. Rat. Mech. An. , vol.173 , Issue.3 , pp. 301-344
    • Patrick, G.W.1    Roberts, M.2    Wulff, C.3
  • 237
    • 85072846014 scopus 로고
    • The Geometry of Topological Stability; LMS Monographs, new ser. 9, Clarendon
    • A. du Plessis and T. Wall: The Geometry of Topological Stability; LMS Monographs, new ser. 9, Clarendon (1995)
    • (1995)
    • du Plessis, A.1    Wall, T.2
  • 240
    • 84990623105 scopus 로고
    • Integrability of Hamiltonian Systems on Cantor Sets
    • p
    • J. Pöschel: Integrability of Hamiltonian Systems on Cantor Sets; Comm. Pure Appl. Math. 35, p. 653–696 (1982)
    • (1982) Comm. Pure Appl. Math. , vol.35 , pp. 653-696
    • Pöschel, J.1
  • 241
    • 0000882204 scopus 로고
    • On Elliptic Lower Dimensional Tori in Hamiltonian Systems
    • p
    • J. Pöschel: On Elliptic Lower Dimensional Tori in Hamiltonian Systems; Math. Z. 202, p. 559–608 (1989)
    • (1989) Math. Z. , vol.202 , pp. 559-608
    • Pöschel, J.1
  • 243
    • 0010778446 scopus 로고
    • Symmetry and bifurcation of fixed points of area preserving maps
    • p
    • R.J. Rimmer: Symmetry and bifurcation of fixed points of area preserving maps; J. Diff. Eq. 29, p. 329–344 (1978)
    • (1978) J. Diff. Eq. , vol.29 , pp. 329-344
    • Rimmer, R.J.1
  • 246
    • 0347301749 scopus 로고    scopus 로고
    • A Cantor set of tori with monodromy near a focus-focus singularity
    • p
    • B. Rink: A Cantor set of tori with monodromy near a focus-focus singularity; Nonlinearity 17, p. 347–356 (2004)
    • (2004) Nonlinearity , vol.17 , pp. 347-356
    • Rink, B.1
  • 247
    • 0000631525 scopus 로고
    • Generic properties of conservative systems
    • p
    • R.C. Robinson: Generic properties of conservative systems; Am. J. Math. 92, p. 562–603 (1970)
    • (1970) Am. J. Math. , vol.92 , pp. 562-603
    • Robinson, R.C.1
  • 248
    • 0000631525 scopus 로고
    • Generic properties of conservative systems II
    • p
    • R.C. Robinson: Generic properties of conservative systems II; Am. J. Math. 92, p. 897–906 (1970)
    • (1970) Am. J. Math. , vol.92 , pp. 897-906
    • Robinson, R.C.1
  • 249
    • 85072835631 scopus 로고    scopus 로고
    • Hamilton–Jacobi method for a simple resonance; preprint
    • M. Rudnev: Hamilton–Jacobi method for a simple resonance; preprint, University of Bristol (2003)
    • (2003) University of Bristol
    • Rudnev, M.1
  • 250
    • 0002583282 scopus 로고
    • Über invariante Kurven differenzierbarer Abbildungen eines Kreisringes
    • p
    • H. Rüssmann: Über invariante Kurven differenzierbarer Abbildungen eines Kreisringes; Nachr. Akad. Wiss. Göttingen, II. Math.-Phys. Kl. 1970(5), p. 67–105 (1970)
    • (1970) Nachr. Akad. Wiss. Göttingen, II. Math.-Phys. Kl. , vol.1970 , Issue.5 , pp. 67-105
    • Rüssmann, H.1
  • 251
    • 0000285454 scopus 로고    scopus 로고
    • Invariant tori in non-degenerate nearly integrable Hamiltonian systems
    • p
    • H. Rüssmann: Invariant tori in non-degenerate nearly integrable Hamiltonian systems; Reg. & Chaot. Dyn. 6(2), p. 119–204 (2001)
    • (2001) Reg. & Chaot. Dyn. , vol.6 , Issue.2 , pp. 119-204
    • Rüssmann, H.1
  • 253
    • 0001597114 scopus 로고    scopus 로고
    • Bifurcation of periodic orbits of Hamiltonian systems: An analysis using normal form theory
    • p
    • D.A. Sadovskií and J.B. Delos: Bifurcation of periodic orbits of Hamiltonian systems: An analysis using normal form theory; Phys. Rev. E 54(2), p. 2033– 2070 (1996)
    • (1996) Phys. Rev. E , vol.54 , Issue.2 , pp. 2033-2070
    • Sadovskií, D.A.1    Delos, J.B.2
  • 254
    • 0001239899 scopus 로고
    • Are higher order resonances really interesting ?
    • p
    • J. Sanders: Are higher order resonances really interesting ? Celest. Mech. 16, p. 421–440 (1978)
    • (1978) Celest. Mech. , vol.16 , pp. 421-440
    • Sanders, J.1
  • 255
    • 0041656295 scopus 로고    scopus 로고
    • Normal form theory and spectral sequences
    • p
    • J. Sanders: Normal form theory and spectral sequences; J. Diff. Eq. 192, p. 536–552 (2003)
    • (2003) J. Diff. Eq. , vol.192 , pp. 536-552
    • Sanders, J.1
  • 257
    • 0000075556 scopus 로고
    • A Regularity Theorem for Conservation Laws
    • p
    • D. Schaeffer: A Regularity Theorem for Conservation Laws; Adv. Math. 11 p. 368–386 (1973)
    • (1973) Adv. Math. , vol.11 , pp. 368-386
    • Schaeffer, D.1
  • 258
    • 85072833325 scopus 로고    scopus 로고
    • Geometry, Mechanics and Dynamics: Volume in honor of the 60th birthday of J.E. Marsden (eds. P. Newton, P. Holmes and A. Weinstein) Springer (2002)
    • J. Scheurle and S. Walcher: On Normal Form Computations; p. 309–325 in: Geometry, Mechanics and Dynamics: Volume in honor of the 60th birthday of J.E. Marsden (eds. P. Newton, P. Holmes and A. Weinstein) Springer (2002)
    • On Normal Form Computations , pp. 309-325
    • Scheurle, J.1    Walcher, S.2
  • 260
    • 0018691508 scopus 로고
    • Bifurcation of higher-dimensional tori
    • p
    • G.R. Sell: Bifurcation of higher-dimensional tori; Arch. Rat. Mech. An. 69(3), p. 199–230 (1979)
    • (1979) Arch. Rat. Mech. An. , vol.69 , Issue.3 , pp. 199-230
    • Sell, G.R.1
  • 262
    • 9444285386 scopus 로고    scopus 로고
    • The classical KAM theory at the dawn of the twenty-first century
    • p
    • M.B. Sevryuk: The classical KAM theory at the dawn of the twenty-first century; Moscow Math. J. 3(3), p. 1113–1144 (2003)
    • (2003) Moscow Math. J. , vol.3 , Issue.3 , pp. 1113-1144
    • Sevryuk, M.B.1
  • 264
    • 0007018954 scopus 로고
    • Singularities of functions on boundaries, corners, etc.; Quart
    • Oxford (2) 32
    • D. Siersma: Singularities of functions on boundaries, corners, etc.; Quart. J. Math. Oxford (2) 32, p. 119–127 (1981)
    • (1981) J. Math. , pp. 119-127
    • Siersma, D.1
  • 265
    • 0001229672 scopus 로고
    • Stratified symplectic spaces and reduction
    • p
    • R. Sjamaar and E. Lerman: Stratified symplectic spaces and reduction; Ann. Math. 134, p. 375–422 (1991)
    • (1991) Ann. Math. , vol.134 , pp. 375-422
    • Sjamaar, R.1    Lerman, E.2
  • 266
    • 0016216299 scopus 로고    scopus 로고
    • On the stability of an autonomous Hamiltonian system with two degrees of freedom in the case of equal frequencies
    • p
    • A.G. Sokol’skii: On the stability of an autonomous Hamiltonian system with two degrees of freedom in the case of equal frequencies; J. appl. Math. Mech. 38(5), p. 741–749 (1974-5)
    • J. Appl. Math. Mech. , vol.38 , Issue.5 , pp. 741-749
    • Sokol’Skii, A.G.1
  • 267
    • 0141669291 scopus 로고
    • Proof of the stability of Lagrangian solutions at a critical relation of masses; Sov
    • p
    • A.G. Sokol’skii: Proof of the stability of Lagrangian solutions at a critical relation of masses; Sov. Astron. Lett. 4(2), p. 79–81 (1978)
    • (1978) Astron. Lett. , vol.4 , Issue.2 , pp. 79-81
    • Sokol’Skii, A.G.1
  • 269
    • 4043050765 scopus 로고    scopus 로고
    • Quantizing the classical cat
    • p
    • I. Stewart: Quantizing the classical cat; Nature 430, p. 731–732 (2004)
    • (2004) Nature , vol.430 , pp. 731-732
    • Stewart, I.1
  • 270
    • 77951931683 scopus 로고
    • 1-counterexample of Mosers’s twist theorem
    • p
    • 1-counterexample of Mosers’s twist theorem; Indag. math. 33, p. 378–386 (1971)
    • (1971) Indag. Math , vol.33 , pp. 378-386
    • Takens, F.1
  • 271
    • 85072838239 scopus 로고
    • Introduction to Global Analysis; Communications 2 of the Mathematical Institute
    • F. Takens: Introduction to Global Analysis; Communications 2 of the Mathematical Institute, Rijksuniversiteit Utrecht (1973)
    • (1973) Rijksuniversiteit Utrecht
    • Takens, F.1
  • 272
    • 85072841286 scopus 로고    scopus 로고
    • Applications of Global Analysis; Communications 3 of the Mathematical Institute, Rijksuniversiteit Utrecht (1974) – reprinted p. 2–61 in Global Analysis of Dynamical Systems, Leiden 2001 (eds. H.W. Broer, B. Krauskopf and G. Vegter) Inst. of Phys. (2001)
    • F. Takens: Forced oscillations and bifurcations; p. 1–59 in Applications of Global Analysis; Communications 3 of the Mathematical Institute, Rijksuniversiteit Utrecht (1974) – reprinted p. 2–61 in Global Analysis of Dynamical Systems, Leiden 2001 (eds. H.W. Broer, B. Krauskopf and G. Vegter) Inst. of Phys. (2001)
    • Forced Oscillations and Bifurcations , pp. 1-59
    • Takens, F.1
  • 273
    • 0039621597 scopus 로고    scopus 로고
    • Resonances in skew and reducible quasiperiodic Hopf bifurcations
    • p
    • F. Takens and F.O.O. Wagener: Resonances in skew and reducible quasiperiodic Hopf bifurcations; Nonlinearity 13, p. 377–396 (2000)
    • (2000) Nonlinearity , vol.13 , pp. 377-396
    • Takens, F.1    Wagener, F.O.O.2
  • 275
    • 3042926459 scopus 로고
    • The mechanism of destruction of resonant tori of Hamiltonian systems
    • p
    • D.V. Treshchëv: The mechanism of destruction of resonant tori of Hamiltonian systems; Math. USSR-Sb. 68, p. 181–203 (1991)
    • (1991) Math. Ussr-Sb. , vol.68 , pp. 181-203
    • Treshchëv, D.V.1
  • 276
    • 0001834024 scopus 로고
    • Hyperbolic tori and asymptotic surfaces in Hamiltonian systems
    • p
    • D.V. Treshchëv: Hyperbolic tori and asymptotic surfaces in Hamiltonian systems; Russ. J. Math. Phys. 2(1), p. 93–110 (1994)
    • (1994) Russ. J. Math. Phys. , vol.2 , Issue.1 , pp. 93-110
    • Treshchëv, D.V.1
  • 277
    • 0002876557 scopus 로고
    • Centre Manifolds, Normal Forms and Elementary Bifurcations
    • p
    • A. Vanderbauwhede: Centre Manifolds, Normal Forms and Elementary Bifurcations; Dynamics Rep. 2, p. 89–169 (1989)
    • (1989) Dynamics Rep , vol.2 , pp. 89-169
    • Vanderbauwhede, A.1
  • 280
  • 281
    • 0036523490 scopus 로고    scopus 로고
    • Bifurcation of a reversible Hamiltonian system from a fixed point with fourfold eigenvalue zero
    • p
    • T. Wagenknecht: Bifurcation of a reversible Hamiltonian system from a fixed point with fourfold eigenvalue zero; Dynamical Systems 17(1), p. 29–44 (2002)
    • (2002) Dynamical Systems , vol.17 , Issue.1 , pp. 29-44
    • Wagenknecht, T.1
  • 283
    • 0042031279 scopus 로고    scopus 로고
    • A note on Gevrey regular KAM theory and the inverse approximation lemma
    • p
    • F.O.O. Wagener: A note on Gevrey regular KAM theory and the inverse approximation lemma; Dynamical Systems 18(2), p. 159–163 (2003)
    • (2003) Dynamical Systems , vol.18 , Issue.2 , pp. 159-163
    • Wagener, F.O.O.1
  • 284
    • 24144464514 scopus 로고    scopus 로고
    • On the quasi-periodic d-fold degenerate bifurcation
    • p
    • F.O.O. Wagener: On the quasi-periodic d-fold degenerate bifurcation; J. Diff. Eq. 216, p. 261–281 (2005)
    • (2005) J. Diff. Eq. , vol.216 , pp. 261-281
    • Wagener, F.O.O.1
  • 286
    • 85072830729 scopus 로고    scopus 로고
    • Geometric properties of generic differentiable manifolds; p. 707– 774 in: Geometry and Topology
    • 1976 (eds. J. Palis and M. do Carmo) LNM 597, Springer (1977)
    • C.T.C. Wall: Geometric properties of generic differentiable manifolds; p. 707– 774 in: Geometry and Topology, Rio de Janeiro 1976 (eds. J. Palis and M. do Carmo) LNM 597, Springer (1977)
    • Rio De Janeiro
    • Wall, C.T.C.1
  • 288
    • 0038109047 scopus 로고
    • Stability of unfoldings in space and time
    • p
    • G. Wassermann: Stability of unfoldings in space and time; Acta math. 135, p. 57–128 (1975)
    • (1975) Acta Math , vol.135 , pp. 57-128
    • Wassermann, G.1
  • 289
    • 85072846527 scopus 로고
    • Classification of singularities with compact Abelian symmetry; Regensburger Math
    • G. Wassermann: Classification of singularities with compact Abelian symmetry; Regensburger Math. Schriften 1 (1977)
    • (1977) Schriften , vol.1
    • Wassermann, G.1
  • 290
    • 0001459972 scopus 로고
    • Normal Modes for Nonlinear Hamiltonian Systems
    • p
    • A. Weinstein: Normal Modes for Nonlinear Hamiltonian Systems; Inv. math. 20, p. 47–57 (1973)
    • (1973) Inv. Math. , vol.20 , pp. 47-57
    • Weinstein, A.1
  • 291
    • 0001705860 scopus 로고
    • Bifurcations and Hamilton’s Principle
    • p
    • A. Weinstein: Bifurcations and Hamilton’s Principle; Math. Z. 159, p. 235– 248 (1978)
    • (1978) Math. Z. , vol.159 , pp. 235-248
    • Weinstein, A.1
  • 292
    • 84972531238 scopus 로고
    • The local structure of Poisson manifolds
    • p
    • A. Weinstein: The local structure of Poisson manifolds; J. Diff. Geom. 18, p. 523–557 (1983)
    • (1983) J. Diff. Geom. , vol.18 , pp. 523-557
    • Weinstein, A.1
  • 294
    • 0035604021 scopus 로고    scopus 로고
    • Persistence of lower-dimensional tori under the first Melnikov’s non-resonance condition
    • p
    • J. Xu and J. You: Persistence of lower-dimensional tori under the first Melnikov’s non-resonance condition; J. Math. Pures Appl. 80(10), p. 1045–1067 (2001)
    • (2001) J. Math. Pures Appl. , vol.80 , Issue.10 , pp. 1045-1067
    • Xu, J.1    You, J.2
  • 296
    • 0032021298 scopus 로고    scopus 로고
    • A KAM Theorem for Hyperbolic-Type Degenerate Lower Dimensional Tori in Hamiltonian Systems
    • p
    • J. You: A KAM Theorem for Hyperbolic-Type Degenerate Lower Dimensional Tori in Hamiltonian Systems; Comm. Math. Phys. 192(1), p. 145–168 (1998)
    • (1998) Comm. Math. Phys. , vol.192 , Issue.1 , pp. 145-168
    • You, J.1
  • 298
    • 84980189959 scopus 로고
    • Generalized Implicit Function Theorems with Applications to Some Small Divisor Problems I
    • p
    • E. Zehnder: Generalized Implicit Function Theorems with Applications to Some Small Divisor Problems I; Comm. Pure Appl. Math. 28, p. 91–140 (1975)
    • (1975) Comm. Pure Appl. Math. , vol.28 , pp. 91-140
    • Zehnder, E.1
  • 299
    • 84980167395 scopus 로고
    • Generalized Implicit Function Theorems With Applications To Some Small Divisor Problems II
    • p
    • E. Zehnder: Generalized Implicit Function Theorems With Applications To Some Small Divisor Problems II; Comm. Pure Appl. Math. 29, p. 49–111 (1976)
    • (1976) Comm. Pure Appl. Math. , vol.29 , pp. 49-111
    • Zehnder, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.