메뉴 건너뛰기




Volumn 13, Issue 1, 2005, Pages 63-102

Renormalization of isoenergetically degenerate hamiltonian flows and associated bifurcations of invariant tori

Author keywords

Invariant tori; Isoenergetically degenerate Hamiltonian flows; Renormalization

Indexed keywords


EID: 18244367382     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2005.13.63     Document Type: Article
Times cited : (18)

References (46)
  • 1
    • 0034349022 scopus 로고    scopus 로고
    • Renormalization and periodic orbits for Hamiltonian flows
    • J. J. Abad, H. Koch, Renormalization and periodic orbits for Hamiltonian flows, Comm. Math. Phys. 212 (2000), 371-394.
    • (2000) Comm. Math. Phys. , vol.212 , pp. 371-394
    • Abad, J.J.1    Koch, H.2
  • 2
    • 0009128788 scopus 로고    scopus 로고
    • A renormalization group for Hamiltonians: Numerical results
    • J. J. Abad, H. Koch and P. Wittwer, A renormalization group for Hamiltonians: numerical results, Nonlinearity 11 (1998), 1185-1194.
    • (1998) Nonlinearity , vol.11 , pp. 1185-1194
    • Abad, J.J.1    Koch, H.2    Wittwer, P.3
  • 5
    • 0000166834 scopus 로고    scopus 로고
    • Hamiltonian nontwist map for magnetic field lines with locally reversed shear in toroidal geometry
    • R. Balescu, Hamiltonian nontwist map for magnetic field lines with locally reversed shear in toroidal geometry, Phys. Rev. E58 (1998), 3781-3792.
    • (1998) Phys. Rev. , vol.E58 , pp. 3781-3792
    • Balescu, R.1
  • 7
    • 0036577358 scopus 로고    scopus 로고
    • Thresholds to chaos and ionization for the hydrogen atom in rotating fields
    • 053402
    • C. Chandre, D. Farrelly and T. Uzer, Thresholds to chaos and ionization for the hydrogen atom in rotating fields, Phys. Rev. A65 053402 (2002), 1-21.
    • (2002) Phys. Rev. , vol.A65 , pp. 1-21
    • Chandre, C.1    Farrelly, D.2    Uzer, T.3
  • 8
    • 0001582465 scopus 로고    scopus 로고
    • Universality for the breakup of invariant tori in Hamiltonian flows
    • C. Chandre, M. Govin, H. R. Jauslin and H. Koch, Universality for the breakup of invariant tori in Hamiltonian flows, Phys. Rev. E67 (1998), 6612-6617.
    • (1998) Phys. Rev. , vol.E67 , pp. 6612-6617
    • Chandre, C.1    Govin, M.2    Jauslin, H.R.3    Koch, H.4
  • 9
    • 0000667908 scopus 로고    scopus 로고
    • Approximate renormalization-group transformation for Hamiltonian systems with three degrees of freedom
    • C. Chandre, H. R. Jauslin, G. Benfatto and A. Celletti, Approximate renormalization-group transformation for Hamiltonian systems with three degrees of freedom, Phys. Rev 60E (1999), 5412-5421.
    • (1999) Phys. Rev , vol.60 E , pp. 5412-5421
    • Chandre, C.1    Jauslin, H.R.2    Benfatto, G.3    Celletti, A.4
  • 11
    • 0027395592 scopus 로고
    • Chaotic transport by Rossby waves in shear flow
    • D. del-Castillo-Negrete, P. J. Morrison, Chaotic transport by Rossby waves in shear flow, Phys. Fluids A5 (1993), 948-965.
    • (1993) Phys. Fluids , vol.A5 , pp. 948-965
    • Del-Castillo-Negrete, D.1    Morrison, P.J.2
  • 12
    • 22244493297 scopus 로고    scopus 로고
    • Area preserving nontwist maps: Periodic orbits and transition to chaos
    • D. del-Castillo-Negrette, J. M. Greene and P. J. Morrison, Area preserving nontwist maps: periodic orbits and transition to chaos, Physica D91 (1996), 1-23.
    • (1996) Physica , vol.D91 , pp. 1-23
    • Del-Castillo-Negrette, D.1    Greene, J.M.2    Morrison, P.J.3
  • 13
    • 0010294123 scopus 로고    scopus 로고
    • Renormalization and transition to chaos in area preserving nontwist maps
    • D. del-Castillo-Negrette, J. M. Greene and P. J. Morrison, Renormalization and transition to chaos in area preserving nontwist maps, Physica D100 (1996), 311-329.
    • (1996) Physica , vol.D100 , pp. 311-329
    • Del-Castillo-Negrette, D.1    Greene, J.M.2    Morrison, P.J.3
  • 14
    • 0034347544 scopus 로고    scopus 로고
    • KAM theory and a partial justification of Greene's criterion for nontwist maps
    • A. Delshams, R. De la Llave, KAM theory and a partial justification of Greene's criterion for nontwist maps, SIAM J. of Math. Anal. 31 (2000), 1235-1269.
    • (2000) SIAM J. of Math. Anal. , vol.31 , pp. 1235-1269
    • Delshams, A.1    De La Llave, R.2
  • 16
    • 0342836392 scopus 로고
    • Renormalization method for computing the threshold of the large-scale stochastic instability in two degrees of freedom Hamiltonian systems
    • D. F. Escande, F. Doveil, Renormalization method for computing the threshold of the large-scale stochastic instability in two degrees of freedom Hamiltonian systems, J. Stat. Phys. 26 (1981), 257-284.
    • (1981) J. Stat. Phys. , vol.26 , pp. 257-284
    • Escande, D.F.1    Doveil, F.2
  • 17
    • 0001816458 scopus 로고
    • Quantitative universality for a class of nonlinear transformations
    • M. J. Feigenbaum, Quantitative universality for a class of nonlinear transformations, J. Stat. Phys. 19 (1978), 25-52.
    • (1978) J. Stat. Phys. , vol.19 , pp. 25-52
    • Feigenbaum, M.J.1
  • 18
    • 0347447535 scopus 로고
    • The universal metric properties of nonlinear transformations
    • M. J. Feigenbaum, The universal metric properties of nonlinear transformations, J. Stat. Phys. 21 (1979), 669-706.
    • (1979) J. Stat. Phys. , vol.21 , pp. 669-706
    • Feigenbaum, M.J.1
  • 19
    • 0037331963 scopus 로고    scopus 로고
    • Regions of instability for non-twist maps
    • J. Franks, P. Le Calvez, Regions of instability for non-twist maps, Erg. Theor. Dyn. Syst. 23 (2003), 111-141.
    • (2003) Erg. Theor. Dyn. Syst. , vol.23 , pp. 111-141
    • Franks, J.1    Le Calvez, P.2
  • 21
    • 4644303304 scopus 로고    scopus 로고
    • Renormalization and shearless invariant tori: Numerical results
    • D. Gaidashev, H. Koch, Renormalization and shearless invariant tori: numerical results, Nonlinearity 17 (2004), 1713-1722.
    • (2004) Nonlinearity , vol.17 , pp. 1713-1722
    • Gaidashev, D.1    Koch, H.2
  • 22
    • 0001128446 scopus 로고    scopus 로고
    • Kolmogorov-Arnold-Moser-renormalization-group analysis of stability in Hamiltonian flows
    • M. Govin, C. Chandre and H. R. Jauslin, Kolmogorov-Arnold-Moser-renormalization-group analysis of stability in Hamiltonian flows, Phys. Rev. Lett. 79 (1997), 3881-3884.
    • (1997) Phys. Rev. Lett. , vol.79 , pp. 3881-3884
    • Govin, M.1    Chandre, C.2    Jauslin, H.R.3
  • 24
    • 0000150451 scopus 로고    scopus 로고
    • Drift wave test particle transport in reversed shear profile
    • W. Horton et al., Drift wave test particle transport in reversed shear profile, Phys. Plasma, 5 (1998), 3910-3935.
    • (1998) Phys. Plasma , vol.5 , pp. 3910-3935
    • Horton, W.1
  • 25
    • 0026631994 scopus 로고
    • Shear reversal and MHD activity during Pellet Enhanced Performance plasmas in JET
    • M. Hugon et al., Shear reversal and MHD activity during Pellet Enhanced Performance plasmas in JET, Nuclear Fusion 32 (1992), 33.
    • (1992) Nuclear Fusion , vol.32 , pp. 33
    • Hugon, M.1
  • 27
    • 0003333448 scopus 로고
    • Rigorous and formal stability of orbits about an oblate planet
    • W. T. Kyner, Rigorous and formal stability of orbits about an oblate planet, Mem. of the Am. Math. Soc. 81 (1968), 1-28.
    • (1968) Mem. of the Am. Math. Soc. , vol.81 , pp. 1-28
    • Kyner, W.T.1
  • 28
    • 0033414175 scopus 로고    scopus 로고
    • A renormalization group for Hamiltonians, with applications to KAM tori
    • H. Koch, A renormalization group for Hamiltonians, with applications to KAM tori, Ergodic Theory Dynam. Systems 19 (1999), 475-521.
    • (1999) Ergodic Theory Dynam. Systems , vol.19 , pp. 475-521
    • Koch, H.1
  • 29
    • 0036014246 scopus 로고    scopus 로고
    • On the renormalization of Hamiltonian flows, and critical invariant tori
    • H. Koch, On the renormalization of Hamiltonian flows, and critical invariant tori, Discrete Contin. Dyn. Syst. 8 (2002), 633-646.
    • (2002) Discrete Contin. Dyn. Syst. , vol.8 , pp. 633-646
    • Koch, H.1
  • 30
    • 85039400671 scopus 로고    scopus 로고
    • A Renormalization group fixed point associated with the breakup of golden invariant tori
    • preprint mp_arc 02-175 (2002), to appear in (special volume on Hamiltonian systems)
    • H. Koch, A Renormalization group fixed point associated with the breakup of golden invariant tori, preprint mp_arc 02-175 (2002), to appear in Discrete Contin. Dynam. Systems (special volume on Hamiltonian systems).
    • Discrete Contin. Dynam. Systems
    • Koch, H.1
  • 32
    • 0000427928 scopus 로고
    • A renormalisation approach to invariant circles in area-preserving maps
    • R. S. MacKay, A renormalisation approach to invariant circles in area-preserving maps, Physica D7 (1983), 283-300.
    • (1983) Physica , vol.D7 , pp. 283-300
    • MacKay, R.S.1
  • 34
    • 0002560832 scopus 로고
    • An approximate renormalization for the break-up of invariant tori with three frequencies
    • R. S. MacKay, J. D. Meiss and J. Stark, An approximate renormalization for the break-up of invariant tori with three frequencies, Phys. Lett. A 190 (1994), 417-424.
    • (1994) Phys. Lett. A , vol.190 , pp. 417-424
    • MacKay, R.S.1    Meiss, J.D.2    Stark, J.3
  • 35
    • 0000535863 scopus 로고
    • Destruction of KAM tori in Hamiltonian systems: Link with the destabilization of nearby cycles and calculation of residues
    • A. Mehr, D.F. Escande, Destruction of KAM tori in Hamiltonian systems: link with the destabilization of nearby cycles and calculation of residues, Physica D13 (1984), 302-338.
    • (1984) Physica , vol.D13 , pp. 302-338
    • Mehr, A.1    Escande, D.F.2
  • 37
    • 0020810173 scopus 로고
    • Universal properties of the transition from guasiperiodicity to chaos in dissipative systems
    • S. Östlund, D. Rand, J. Sethna and E. Siggia, Universal properties of the transition from guasiperiodicity to chaos in dissipative systems, Physica 8D (1983), 303-342.
    • (1983) Physica , vol.8 D , pp. 303-342
    • Östlund, S.1    Rand, D.2    Sethna, J.3    Siggia, E.4
  • 39
    • 0000296339 scopus 로고
    • Critical behavior of a KAM surface. I. Empirical results
    • S. J. Shenker, L. P. Kadanoff, Critical behavior of a KAM surface. I. Empirical results, J. Stat. Phys. 27 (1982), 631-656.
    • (1982) J. Stat. Phys. , vol.27 , pp. 631-656
    • Shenker, S.J.1    Kadanoff, L.P.2
  • 40
    • 0014883327 scopus 로고
    • A method for mapping a toroidal magnetic field by storage of phase stabilized electrons
    • R. M. Sinclair, J. C. Hosea and G. V. Sheffield, A method for mapping a toroidal magnetic field by storage of phase stabilized electrons, Rev. Sci. Instruments 41 (1970), 1552-1559.
    • (1970) Rev. Sci. Instruments , vol.41 , pp. 1552-1559
    • Sinclair, R.M.1    Hosea, J.C.2    Sheffield, G.V.3
  • 41
    • 0004899628 scopus 로고
    • Current penetration and plasma disruption
    • T. H. Stix, Current penetration and plasma disruption, Phys. Rev. Lett. 36 (1976), 521-524.
    • (1976) Phys. Rev. Lett. , vol.36 , pp. 521-524
    • Stix, T.H.1
  • 42
    • 0002070251 scopus 로고
    • The birth process of periodic orbits in nontwist maps
    • J.P. Van der Weele, T.P. Valkering, The birth process of periodic orbits in nontwist maps, Physica A169 (1990), 42-72.
    • (1990) Physica , vol.A169 , pp. 42-72
    • Van Der Weele, J.P.1    Valkering, T.P.2
  • 43
    • 0001012531 scopus 로고
    • The birth of twin Poincar-Birkhoff chains near 1:3 resonance
    • J.P. Van der Weele, T.P. Valkering, H.W. Kapel and T. Post, The birth of twin Poincar-Birkhoff chains near 1:3 resonance, Physica A153 (1988), 283-294.
    • (1988) Physica , vol.A153 , pp. 283-294
    • Van Der Weele, J.P.1    Valkering, T.P.2    Kapel, H.W.3    Post, T.4
  • 44
    • 85039389828 scopus 로고
    • Confinement in toroidal systems with partially destroyed magnetic surfaces
    • IAEA-CN-41/T-3
    • R. B. White et al., Confinement in toroidal systems with partially destroyed magnetic surfaces, IAEA conference proceedings, IAEA-CN-41/T-3 (1982).
    • (1982) IAEA Conference Proceedings
    • White, R.B.1
  • 45
    • 33645916042 scopus 로고
    • Renormalization group and critical phenomena. I. Renormalization group and the Kadanoff scaling picture
    • K. Wilson, Renormalization group and critical phenomena. I. Renormalization group and the Kadanoff scaling picture, Phys. Rev. B4 (1971), 3174-3183.
    • (1971) Phys. Rev. , vol.B4 , pp. 3174-3183
    • Wilson, K.1
  • 46
    • 26144461489 scopus 로고
    • Renormalization group and critical phenomena. II. Phase-space cell analysis of critical behavior
    • K. Wilson, Renormalization group and critical phenomena. II. Phase-space cell analysis of critical behavior, Phys. Rev. B4 (1971), 3184-3205.
    • (1971) Phys. Rev. , vol.B4 , pp. 3184-3205
    • Wilson, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.