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Volumn 1864, Issue , 2005, Pages 1-151

Metamorphoses of hamiltonian systems with symmetries

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EID: 33748949958     PISSN: 00758434     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Article
Times cited : (50)

References (138)
  • 2
    • 0000260141 scopus 로고
    • The geometry of spontaneous symmetry breaking
    • M. Abud and G. Sartori. The geometry of spontaneous symmetry breaking. Annals of Physics, 150:307-372, 1983.
    • (1983) Annals of Physics , vol.150 , pp. 307-372
    • Abud, M.1    Sartori, G.2
  • 3
    • 3042533231 scopus 로고    scopus 로고
    • Quantum monodromy for diatomic molecules in combined electrostatic and pulsed nonresonant laser fields
    • C. A. Arango, W. W. Kennerly, and G. S. Ezra. Quantum monodromy for diatomic molecules in combined electrostatic and pulsed nonresonant laser fields. Chem. Phys. Lett., 392:486-492, 2004.
    • (2004) Chem. Phys. Lett. , vol.392 , pp. 486-492
    • Arango, C.A.1    Kennerly, W.W.2    Ezra, G.S.3
  • 4
    • 33748939725 scopus 로고
    • Reduction of Hamiltonian systems for singular values of momentum
    • J. Arms. Reduction of Hamiltonian systems for singular values of momentum. Contemporary Math., 81:99-110, 1988.
    • (1988) Contemporary Math. , vol.81 , pp. 99-110
    • Arms, J.1
  • 5
    • 0002941145 scopus 로고
    • Geometric and algebraic reduction for singular momentum mappings
    • J. Arms, M. Gotay, and G. Jennings. Geometric and algebraic reduction for singular momentum mappings. Advances in Mathematics, 74:43-103, 1990.
    • (1990) Advances in Mathematics , vol.74 , pp. 43-103
    • Arms, J.1    Gotay, M.2    Jennings, G.3
  • 6
    • 0000752863 scopus 로고
    • Symmetry and bifurcations of momentum mappings
    • J. Arms, J. Marsden, and V. Moncrief. Symmetry and bifurcations of momentum mappings. Comm. Math. Physics, 78:455-478, 1981.
    • (1981) Comm. Math. Physics , vol.78 , pp. 455-478
    • Arms, J.1    Marsden, J.2    Moncrief, V.3
  • 7
    • 0011690795 scopus 로고
    • Reduction procedures for Poisson manifolds
    • P. Donato et al., editor', Birkhaäuser, Boston
    • J. Arms and D. Wilbour. Reduction procedures for Poisson manifolds. In P. Donato et al., editor', Symplectic geometry and mathematical physics, pages 462-475. Birkhaäuser, Boston, 1991.
    • (1991) Symplectic Geometry and Mathematical Physics , pp. 462-475
    • Arms, J.1    Wilbour, D.2
  • 8
    • 0002881562 scopus 로고
    • A universal reduction procedure for Hamiltonian group actions
    • T. Ratiu, editor, Springer, New York
    • J. M. Arms, R. H. Gushman, and M. J. Gotay. A universal reduction procedure for Hamiltonian group actions. In T. Ratiu, editor, The geometry of Hamiltonian systems, pages 33-51. Springer, New York, 1991.
    • (1991) The Geometry of Hamiltonian Systems , pp. 33-51
    • Arms, J.M.1    Gushman, R.H.2    Gotay, M.J.3
  • 9
    • 0002764805 scopus 로고
    • Proof of a theorem of A.N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the hamiltonian
    • 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. Russian Math. Surveys, 18(5):9-36, 1963.
    • (1963) Russian Math. Surveys , vol.18 , Issue.5 , pp. 9-36
    • Arnol'd, V.I.1
  • 10
    • 33748924810 scopus 로고
    • Mathematical methods of classical mechanics, Springer-Verlag, New York, 2nd edition, Translated by K. Vogtmann and A. Weinstein
    • V. I. Arnol'd. Mathematical methods of classical mechanics, volume 60 of Graduated Texts in Mathematics. Springer-Verlag, New York, 2nd edition, 1989. Translated by K. Vogtmann and A. Weinstein:
    • (1989) Graduated Texts in Mathematics , vol.60
    • Arnol'd, V.I.1
  • 14
    • 0001541212 scopus 로고    scopus 로고
    • Proper group actions and symplectic stratified spaces
    • L. Bates and E. Lerman. Proper group actions and symplectic stratified spaces. Pacific J. Math., 181:201-229, 1997.
    • (1997) Pacific J. Math. , vol.181 , pp. 201-229
    • Bates, L.1    Lerman, E.2
  • 15
    • 0000200040 scopus 로고
    • Degeneration of Hamiltonian monodromy cycles
    • L. Bates and M. Zou. Degeneration of Hamiltonian monodromy cycles. Nonlinearity, 6:313-335, 1993.
    • (1993) Nonlinearity , vol.6 , pp. 313-335
    • Bates, L.1    Zou, M.2
  • 16
    • 33748940227 scopus 로고    scopus 로고
    • The complex geometry of the spherical pendulum
    • F. Beukers and R. Cushman, The complex geometry of the spherical pendulum. Contemporary Math., 292:47-70, 2002.
    • (2002) Contemporary Math. , vol.292 , pp. 47-70
    • Beukers, F.1    Cushman, R.2
  • 18
    • 33748936099 scopus 로고    scopus 로고
    • Bifurcations in Hamiltonian systems: computing singularities by Gröbner bases, Springer-Verlag, Berlin
    • H. Broer, I. Hoveijn, G. Lunter, and G. Vegter. Bifurcations in Hamiltonian systems: computing singularities by Gröbner bases, volume 1806 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 2003.
    • (2003) Lecture Notes in Mathematics , vol.1806
    • Broer, H.1    Hoveijn, I.2    Lunter, G.3    Vegter, G.4
  • 19
    • 0242371831 scopus 로고    scopus 로고
    • The geometry of resonance tongues: A singularity theory approach
    • H. W. Broer, M. Golubitsky, and G. Vegter. The geometry of resonance tongues: a singularity theory approach. Nonlinearity, 16:1511-1538, 2003.
    • (2003) Nonlinearity , vol.16 , pp. 1511-1538
    • Broer, H.W.1    Golubitsky, M.2    Vegter, G.3
  • 20
    • 0033196198 scopus 로고    scopus 로고
    • The inverted pendulum: A singularity theory approach
    • H. W. Broer, I. Hoveijn, M. van Noort. and G. Vegter. The inverted pendulum: a singularity theory approach. J. Diff. Eq., 157:120-149, 1999.
    • (1999) J. Diff. Eq. , vol.157 , pp. 120-149
    • Broer, H.W.1    Hoveijn, I.2    Van Noort, M.3    Vegter, G.4
  • 21
    • 22244480073 scopus 로고    scopus 로고
    • Equivariant singularity with distinguished parameters, two case studies of resonant Hamiltonian systems
    • H. W. Broer, G. A. Lunter, and G. Vegter. Equivariant singularity with distinguished parameters, two case studies of resonant Hamiltonian systems. Physica D, 112:64-80, 1997.
    • (1997) Physica D , vol.112 , pp. 64-80
    • Broer, H.W.1    Lunter, G.A.2    Vegter, G.3
  • 22
    • 0041555010 scopus 로고
    • Trojan satellites-limiting case
    • D. Buchanan. Trojan satellites-limiting case. Trans. R. Soc. Canada, 35:9-25, 1941.
    • (1941) Trans. R. Soc. Canada , vol.35 , pp. 9-25
    • Buchanan, D.1
  • 23
    • 0001556435 scopus 로고
    • On averaging, reduction and symmetry in Hamiltonian systems
    • R. C. Churchill, M. Kummer, and D. L. Rod. On averaging, reduction and symmetry in Hamiltonian systems. J. Diff. Eqns., 49:359-414, 1983.
    • (1983) J. Diff. Eqns. , vol.49 , pp. 359-414
    • Churchill, R.C.1    Kummer, M.2    Rod, D.L.3
  • 24
    • 0002768325 scopus 로고
    • A survey of the Henon-Heiles Hamiltonian with applications to related examples
    • G. Casati and J. Ford, editors, Stochastic behavior in classical, and quantum Hamiltonian systems, Berlin. . Springer
    • R. C. Churchill, G. Pecelli, and D. L. Rod. A survey of the Henon-Heiles Hamiltonian with applications to related examples. In G. Casati and J. Ford, editors, Stochastic behavior in classical, and quantum Hamiltonian systems, volume 93 of Lecture, Notes in Physics, pages 76-136, Berlin. 1979. Springer.
    • (1979) Lecture, Notes in Physics , vol.93 , pp. 76-136
    • Churchill, R.C.1    Pecelli, G.2    Rod, D.L.3
  • 26
    • 0003071805 scopus 로고
    • Normal form for Hamiltonian vector fields with periodic flow
    • S. Sternberg, editor, Reidel, Dordrecht
    • R. Cushman. Normal form for Hamiltonian vector fields with periodic flow, in S. Sternberg, editor, Differential geometric methods in mathematical physics. pages 125-144. Reidel, Dordrecht, 1984.
    • (1984) Differential Geometric Methods in Mathematical Physics , pp. 125-144
    • Cushman, R.1
  • 27
    • 0039789453 scopus 로고
    • On singular reduction of Hamiltonian spaces
    • P. Donato et al., editor, Birkhaäuser, Boston
    • R. Cushman and R. Sjamaar. On singular reduction of Hamiltonian spaces. In P. Donato et al., editor, Symplectic geometry and mathematical physics, pages 114-128. Birkhaäuser, Boston, 1991.
    • (1991) Symplectic Geometry and Mathematical Physics , pp. 114-128
    • Cushman, R.1    Sjamaar, R.2
  • 28
    • 0035622635 scopus 로고    scopus 로고
    • Differential structure of orbit spaces
    • R. Cushman and J. Sniatycki. Differential structure of orbit spaces. Canad. J. Math., 53:715-755, 2001.
    • (2001) Canad. J. Math. , vol.53 , pp. 715-755
    • Cushman, R.1    Sniatycki, J.2
  • 29
    • 0009206017 scopus 로고
    • A survey of normalization techniques applied to perturbed Keplerian systems
    • K. Jones et al, editor, Dynamics Reported, New York, . Springer-Verlag
    • R. H. Cushman. A survey of normalization techniques applied to perturbed Keplerian systems. In K. Jones et al, editor, Dynamics Reported, volume 1 of new series, pages 54-112, New York, 1991. Springer-Verlag.
    • (1991) New Series , vol.1 , pp. 54-112
    • Cushman, R.H.1
  • 32
    • 0033099574 scopus 로고    scopus 로고
    • Singular reduction of axially symmetric perturbations of the isotropic harmonic oscillator
    • R. H. Cushman, R. Ferrer, and H. Hanßmann. Singular reduction of axially symmetric perturbations of the isotropic harmonic oscillator. Nonlinearity, 12:389-410, 1999.
    • (1999) Nonlinearity , vol.12 , pp. 389-410
    • Cushman, R.H.1    Ferrer, R.2    Hanßmann, H.3
  • 33
    • 0033153845 scopus 로고    scopus 로고
    • Monodromy perturbed Kepler systems: Hydrogen atom in crossed fields
    • R. H. Cushman and D. A. Sadovskií. Monodromy perturbed Kepler systems: hydrogen atom in crossed fields. Europhysics Letters. 47:1-7, 1999.
    • (1999) Europhysics Letters. , vol.47 , pp. 1-7
    • Cushman, R.H.1    Sadovskií, D.A.2
  • 34
    • 0347450519 scopus 로고    scopus 로고
    • Monodromy in the hydrogen atom in crossed fields
    • R. H. Cushman and D. A. Sadovskií. Monodromy in the hydrogen atom in crossed fields. Physica D, 142:166-196, 2000.
    • (2000) Physica D , vol.142 , pp. 166-196
    • Cushman, R.H.1    Sadovskií, D.A.2
  • 35
    • 0007019484 scopus 로고
    • The Hamiltonian Hopf bifurcation in the Lagrange top
    • Springer-Verlag
    • R. H. Cushman and J. C. van der Meer. The Hamiltonian Hopf bifurcation in the Lagrange top. In Lecture Notes in Mathematics, volume 1416, pages 26-38. Springer-Verlag, 1991.
    • (1991) Lecture Notes in Mathematics , vol.1416 , pp. 26-38
    • Cushman, R.H.1    Van Der Meer, J.C.2
  • 36
    • 0036434806 scopus 로고    scopus 로고
    • Sign of the monodromy for Liouville integrable systems
    • R. H. Cushman and S. Vu Ngoc. Sign of the monodromy for Liouville integrable systems. Ann. Henri Poincaré, 3:883-894, 2002.
    • (2002) Ann. Henri Poincaré , vol.3 , pp. 883-894
    • Cushman, R.H.1    Vu Ngoc, S.2
  • 37
    • 0000717287 scopus 로고
    • Canonical transformations depending on a small parameter
    • A. Deprit. Canonical transformations depending on a small parameter. Cel. Mech., 1:12-30, 1969.
    • (1969) Cel. Mech. , vol.1 , pp. 12-30
    • Deprit, A.1
  • 39
    • 84980167278 scopus 로고
    • On global action-angle coordinates
    • J. J. Duistermaat. On global action-angle coordinates. Comm. Pure Appl. Math., 33:687-706, 1980.
    • (1980) Comm. Pure Appl. Math. , vol.33 , pp. 687-706
    • Duistermaat, J.J.1
  • 40
    • 0003282826 scopus 로고
    • Bifurcations of periodic solutions near equilibrium points of Hamiltonian systems
    • preprint 300. Dept. of Mathematics, University of Utrecht, August 1983. 6 lectures given at the CIME course on Montecatini Terme, Italy
    • J. J. Duistermaat. Bifurcations of periodic solutions near equilibrium points of Hamiltonian systems, preprint 300. Dept. of Mathematics, University of Utrecht, August 1983. 6 lectures given at the CIME course on Bifurcation theory and applications, Montecatini Terme, Italy, 1983.
    • (1983) Bifurcation Theory and Applications
    • Duistermaat, J.J.1
  • 41
    • 0032340303 scopus 로고    scopus 로고
    • The monodromy in the Hamiltonian Hopf bifurcation
    • J. J. Duistermaat. The monodromy in the Hamiltonian Hopf bifurcation. Z. Angew. Math. Phys., 49:156-161, 1998.
    • (1998) Z. Angew. Math. Phys. , vol.49 , pp. 156-161
    • Duistermaat, J.J.1
  • 42
    • 34250229086 scopus 로고
    • On the variation in the cohomology of the symplectic form of the reduced phase space
    • J. J. Duistermaat and G. J. Heckman. On the variation in the cohomology of the symplectic form of the reduced phase space. Inventiones mathematicae, 69:259-268, 1982.
    • (1982) Inventiones Mathematicae , vol.69 , pp. 259-268
    • Duistermaat, J.J.1    Heckman, G.J.2
  • 43
    • 0346057757 scopus 로고
    • Addendum to "On the variation in the cohomology of the symplectic form of the reduced phase space"
    • J. J. Duistermaat and G. J. Heckman. Addendum to "On the variation in the cohomology of the symplectic form of the reduced phase space". Inventiones mathematicae, 72:153-158, 1983.
    • (1983) Inventiones Mathematicae , vol.72 , pp. 153-158
    • Duistermaat, J.J.1    Heckman, G.J.2
  • 45
    • 2942585296 scopus 로고    scopus 로고
    • Hamiltonian Hopf bifurcation of the hydrogen atom in crossed fields
    • K. Efstathiou, R. H. Cushman, and D. A. Sadovskií. Hamiltonian Hopf bifurcation of the hydrogen atom in crossed fields. Physica D, 194:250-274, 2004. http://www.elsevier.com/locate/physd.
    • (2004) Physica D , vol.194 , pp. 250-274
    • Efstathiou, K.1    Cushman, R.H.2    Sadovskií, D.A.3
  • 46
    • 2542499014 scopus 로고    scopus 로고
    • Global bending quantum number and the absence of monodromy in the HCN↔CNH molecule
    • K. Efstathiou, M. Joyeux, and D. A. Sadovskií. Global bending quantum number and the absence of monodromy in the HCN↔CNH molecule. Phys. Rev. A, 69:032504, 2004.
    • (2004) Phys. Rev. A , vol.69 , pp. 032504
    • Efstathiou, K.1    Joyeux, M.2    Sadovskií, D.A.3
  • 47
    • 1642271533 scopus 로고    scopus 로고
    • Perturbations of the 1:1:1 resonance with tetrahedral symmetry: A three degree of freedom analogue of the two degree of freedom Hénon-Heiles Hamiltonian
    • K. Efstathiou and D. A. Sadovskiiź. Perturbations of the 1:1:1 resonance with tetrahedral symmetry: a three degree of freedom analogue of the two degree of freedom Hénon-Heiles Hamiltonian. Nonlinearity, 17:415-446, 2004. http://www.iop.org/nlin/.
    • (2004) Nonlinearity , vol.17 , pp. 415-446
    • Efstathiou, K.1    Sadovskiiź, D.A.2
  • 48
    • 1542407759 scopus 로고    scopus 로고
    • Linear Hamiltonian Hopf bifurcation for point group invariant perturbations of the 1:1:1 resonance
    • 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. Roy. Soc. London. Scr. A, 459:2997-3019, 2003.
    • (2003) Proc. Roy. Soc. London. Scr. A , vol.459 , pp. 2997-3019
    • Efstathiou, K.1    Sadovskií, D.A.2    Cushman, R.H.3
  • 49
    • 4243187109 scopus 로고    scopus 로고
    • Analysis of rotationvibration relative equilibria on the example of a tetrahedral four atom molecule
    • K. Efstathiou, D. A. Sadovskií, and B. I. Zhilinskií. Analysis of rotationvibration relative equilibria on the example of a tetrahedral four atom molecule. SIAM J. Appl. Dyn. Syst. (SIADS), 3:261-351, 2004.
    • (2004) SIAM J. Appl. Dyn. Syst. (SIADS) , vol.3 , pp. 261-351
    • Efstathiou, K.1    Sadovskií, D.A.2    Zhilinskií, B.I.3
  • 50
    • 0001623241 scopus 로고
    • An SCF potential energy surface for Lithium Cyanide
    • R. Essers, J. Tennyson, and P. E. S. Wormer. An SCF potential energy surface for Lithium Cyanide. Chem. Phys. Lett., 89:223-227, 1982.
    • (1982) Chem. Phys. Lett. , vol.89 , pp. 223-227
    • Essers, R.1    Tennyson, J.2    Wormer, P.E.S.3
  • 51
    • 0043161218 scopus 로고
    • Dynamical symmetry of the quadratic Zeeman effect in hydrogen: Semiclassical quantization
    • D. Farrelly and K. Krantzman. Dynamical symmetry of the quadratic Zeeman effect in hydrogen: Semiclassical quantization. Phys. Rev. A, 43:1666-1668, 1991.
    • (1991) Phys. Rev. A , vol.43 , pp. 1666-1668
    • Farrelly, D.1    Krantzman, K.2
  • 52
    • 0009209977 scopus 로고
    • Action-angle variables for the diamagnetic Kepler problem
    • D. Farrelly and J. A. Milligan. Action-angle variables for the diamagnetic Kepler problem. Phys. Rev. A, 45:8277-8279, 1992.
    • (1992) Phys. Rev. A , vol.45 , pp. 8277-8279
    • Farrelly, D.1    Milligan, J.A.2
  • 53
    • 0001580637 scopus 로고
    • Electronic structure of Rydberg atoms in parallel electric and magnetic fields
    • D. Farrelly, T. Uzer, P. E. Raines, J. P. Skelton, and J. A. Milligan. Electronic structure of Rydberg atoms in parallel electric and magnetic fields. Phys. Rev. A, 45:4738-4751, 1992.
    • (1992) Phys. Rev. A , vol.45 , pp. 4738-4751
    • Farrelly, D.1    Uzer, T.2    Raines, P.E.3    Skelton, J.P.4    Milligan, J.A.5
  • 54
    • 0032093326 scopus 로고    scopus 로고
    • The Hénon and Heiles problem in three dimensions, I. Periodic orbits near the origin
    • S. Ferrer, M. Lara, J. Palacián, J, F. San Juan, A. Viartola, and P. Yanguas. The Hénon and Heiles problem in three dimensions, I. Periodic orbits near the origin. Int. J. Bif. Chaos, 8:1199-1213, 1998.
    • (1998) Int. J. Bif. Chaos , vol.8 , pp. 1199-1213
    • Ferrer, S.1    Lara, M.2    Palacián, J.3    Juan, F.S.4    Viartola, A.5    Yanguas, P.6
  • 55
    • 0032094211 scopus 로고    scopus 로고
    • The Hénon and Heiles problem in three dimensions. 11. Relative equilibria, and bifurcations in the reduced system
    • S. Ferrer. M. Lara, J. Palacián, J. F. San Juan, A. Viartola, and P. Yanguas. The Hénon and Heiles problem in three dimensions. 11. Relative equilibria, and bifurcations in the reduced system. Int. J. Bif. Chaos, 8:1215-1229, 1998.
    • (1998) Int. J. Bif. Chaos , vol.8 , pp. 1215-1229
    • Ferrer, S.1    Lara, M.2    Palacián, J.3    Juan, J.F.S.4    Viartola, A.5    Yanguas, P.6
  • 56
    • 0028463762 scopus 로고
    • The Kepler ellipses of the hydrogen atom in crossed electric and magnetic fields
    • E. Flöthmann, J. Main, and K. H. Welge. The Kepler ellipses of the hydrogen atom in crossed electric and magnetic fields. J. Phys. B, 27(13):2821-2833, 1994.
    • (1994) J. Phys. B , vol.27 , Issue.13 , pp. 2821-2833
    • Flöthmann, E.1    Main, J.2    Welge, K.H.3
  • 57
    • 0043067821 scopus 로고    scopus 로고
    • Crossed-field hydrogen atom and the three-body Sun-Earth-Moon problem
    • E. Flöthmann and K. H. Welge. Crossed-field hydrogen atom and the three-body Sun-Earth-Moon problem. Phys. Rev. A, 54:1884-1888, 1996.
    • (1996) Phys. Rev. A , vol.54 , pp. 1884-1888
    • Flöthmann, E.1    Welge, K.H.2
  • 59
    • 0003437218 scopus 로고
    • Addison-Wesley Publishing Company, Inc., 2nd edition
    • H. Goldstein. Classical Mechanics. Addison-Wesley Publishing Company, Inc., 2nd edition, 1980.
    • (1980) Classical Mechanics
    • Goldstein, H.1
  • 60
    • 0001855683 scopus 로고
    • The constrained Liapunov-Schmidt procedure and periodic orbits
    • number 4 in Fields Institute Communications, Amer. Math. Soc.
    • M. Golubitsky, J. Marsden, J. Stewart, and M. Dellnitz. The constrained Liapunov-Schmidt procedure and periodic orbits. In Normal forms and homoclinic chaos, number 4 in Fields Institute Communications, pages 81-127. Amer. Math. Soc., 1995.
    • (1995) Normal Forms and Homoclinic Chaos , pp. 81-127
    • Golubitsky, M.1    Marsden, J.2    Stewart, J.3    Dellnitz, M.4
  • 61
    • 0003483217 scopus 로고
    • Singularities and Groups in Bifurcation Theory vol. 1, Springer-Verlag
    • M. Golubitsky and D. Schaeffer. Singularities and Groups in Bifurcation Theory vol. 1, volume 51 of Appl. Math. Sciences. Springer-Verlag, 1985.
    • (1985) Appl. Math. Sciences , vol.51
    • Golubitsky, M.1    Schaeffer, D.2
  • 62
    • 0003483217 scopus 로고
    • Singularities and Groups in Bifurcation Theory vol. 2, Springer-Verlag
    • M. Golubitsky, I. Stewart, and D. Schaeffer. Singularities and Groups in Bifurcation Theory vol. 2, volume 69 of Appl. Math. Sciences. Springer-Verlag, 1988.
    • (1988) Appl. Math. Sciences , vol.69
    • Golubitsky, M.1    Stewart, I.2    Schaeffer, D.3
  • 63
    • 84972572437 scopus 로고
    • Singular angular momentum mappings
    • M. Gotay and L. Bos. Singular angular momentum mappings. J. Diff. Geom., 24:181-203, 1986.
    • (1986) J. Diff. Geom. , vol.24 , pp. 181-203
    • Gotay, M.1    Bos, L.2
  • 68
    • 33748919070 scopus 로고    scopus 로고
    • Algebraic methods for determining Hamiltonian Hopf bifurcations in three-degree-of-freedom systems
    • Technische Universiteit Eindhoven
    • H. Hanßmann and J. C. van der Meer. Algebraic methods for determining Hamiltonian Hopf bifurcations in three-degree-of-freedom systems. Technical Report RANA 03-14, Technische Universiteit Eindhoven, 2003.
    • (2003) Technical Report , vol.RANA 03-14
    • Hanßmann, H.1    Van Der Meer, J.C.2
  • 70
    • 50549163806 scopus 로고
    • 4 molecules. I. Theory of spherical top molecules
    • 4 molecules. I. Theory of spherical top molecules. J. Mol. Spectrosc., 5:355-389, 1960.
    • (1960) J. Mol. Spectrosc. , vol.5 , pp. 355-389
    • Hecht, K.T.1
  • 71
    • 0002519122 scopus 로고
    • The applicability of the third integral of motion: Some numerical experiments
    • M. Hénon and C. Heiles. The applicability of the third integral of motion: some numerical experiments. Astron. J., 69:69-73, 1964.
    • (1964) Astron. J. , vol.69 , pp. 69-73
    • Hénon, M.1    Heiles, C.2
  • 73
    • 0043161231 scopus 로고
    • Semiclassical mechanics of the quadratic Zeeman effect
    • K. D. Krantzman, J. A. Milligan, and D. Farrelly. Semiclassical mechanics of the quadratic Zeeman effect, Phys. Rev. A, 45:3093-3103, 1992.
    • (1992) Phys. Rev. A , vol.45 , pp. 3093-3103
    • Krantzman, K.D.1    Milligan, J.A.2    Farrelly, D.3
  • 74
    • 84936358059 scopus 로고
    • Perturbation theory of Kepler motion based on spinor regularization
    • P. Kustaanheimo and E. Stiefel, Perturbation theory of Kepler motion based on spinor regularization. J. Reine, Angew. Math., 219:204-219, 1965.
    • (1965) J. Reine, Angew. Math. , vol.219 , pp. 204-219
    • Kustaanheimo, P.1    Stiefel, E.2
  • 75
    • 23044508741 scopus 로고
    • Derivation and quantisation of Solov'ev's constant for the diamagnetic Kepler motion
    • M. Kuwata, A. Harada, and H. Hasegawa, Derivation and quantisation of Solov'ev's constant for the diamagnetic Kepler motion. J. Phys. A, 23(14):3227-3244, 1990.
    • (1990) J. Phys. A , vol.23 , Issue.14 , pp. 3227-3244
    • Kuwata, M.1    Harada, A.2    Hasegawa, H.3
  • 76
    • 0000388063 scopus 로고
    • Examples of singular reduction
    • D. Salamon, editor, Cambridge University Press, Cambridge
    • R. Lerman, E. Montgomery, and R. Sjamaar. Examples of singular reduction. In D. Salamon, editor, Symplectic geometry, pages 127-155. Cambridge University Press, Cambridge, 1993.
    • (1993) Symplectic Geometry , pp. 127-155
    • Lerman, R.1    Montgomery, E.2    Sjamaar, R.3
  • 77
    • 0002024654 scopus 로고
    • Sur la régularisation du problème des trois corps
    • T. Levi-Civita. Sur la régularisation du problème des trois corps. Acta Mathematica, 42:99-144, 1920.
    • (1920) Acta Mathematica , vol.42 , pp. 99-144
    • Levi-Civita, T.1
  • 78
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flow
    • E. N. Lorentz. Deterministic nonperiodic flow. J. Atmos. Sci., 20:130-141, 1963.
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130-141
    • Lorentz, E.N.1
  • 79
    • 0002455940 scopus 로고
    • Eckart vectors, Eckart frames and polyatomic molecules
    • J. D. Louck and H. W. Galbraith. Eckart vectors, Eckart frames and polyatomic molecules. Rev. Modern Phys., 48:69-106, 1976.
    • (1976) Rev. Modern Phys. , vol.48 , pp. 69-106
    • Louck, J.D.1    Galbraith, H.W.2
  • 80
    • 33748937359 scopus 로고
    • Problème general de stabilité du mouvement
    • M. A. Lyapunov. Problème general de stabilité du mouvement. Princeton University Press, pages 375-392, 1949.
    • (1949) Princeton University Press , pp. 375-392
    • Lyapunov, M.A.1
  • 82
    • 49549151837 scopus 로고
    • Reduction of symplectic manifolds with symmetry
    • J. Marsden and A. Weinstein. Reduction of symplectic manifolds with symmetry. Rep. Math. Phys., 5:121-130, 1974.
    • (1974) Rep. Math. Phys. , vol.5 , pp. 121-130
    • Marsden, J.1    Weinstein, A.2
  • 83
    • 0042676704 scopus 로고    scopus 로고
    • Comments on the history, theory, and applications of symplectic reduction
    • N. P. Landsman, M. Pflaum, and M. Schlichenmaier, editors, Quantization of singular symplectic quotients, Birkhäuser, Boston
    • J. E. Marsden and A. Weinstein. Comments on the history, theory, and applications of symplectic reduction. In N. P. Landsman, M. Pflaum, and M. Schlichenmaier, editors, Quantization of singular symplectic quotients, volume 198 of Progress in Mathematics, pages 1-10. Birkhäuser, Boston, 2001.
    • (2001) Progress in Mathematics , vol.198 , pp. 1-10
    • Marsden, J.E.1    Weinstein, A.2
  • 84
    • 0002681954 scopus 로고
    • Symmetries and integrals in mechanics
    • M. Peixoto, editor, Academic Press, New York
    • K. R. Meyer. Symmetries and integrals in mechanics. In M. Peixoto, editor, Dynamical systems, pages 259-273. Academic Press, New York, 1973.
    • (1973) Dynamical Systems , pp. 259-273
    • Meyer, K.R.1
  • 85
    • 85009432615 scopus 로고    scopus 로고
    • Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, Springer-erlag. New York
    • K. R. Meyer and G. R. Hall. Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, volume 90 of Applied Mathematical Sciences. Springer-Verlag. New York, 1991.
    • Applied Mathematical Sciences , vol.90 , pp. 1991
    • Meyer, K.R.1    Hall, G.R.2
  • 86
    • 0003582535 scopus 로고
    • Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, Springer-Verlag, New York
    • K. R. Meyer and G. R. Hall. Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, volume 90 of AMS. Springer-Verlag, New York, 1992.
    • (1992) AMS , vol.90
    • Meyer, K.R.1    Hall, G.R.2
  • 87
    • 0002052233 scopus 로고
    • 4 for mass ratios near the critical mass ratio of Routh
    • 4 for mass ratios near the critical mass ratio of Routh. Cel. Mech., 4:99-109, 1971.
    • (1971) Cel. Mech. , vol.4 , pp. 99-109
    • Meyer, K.R.1    Schmidt, D.S.2
  • 88
    • 0010912802 scopus 로고
    • Points critiques des fonctions invariantes sur une G-varieté
    • L. Michel. Points critiques des fonctions invariantes sur une G-varieté. C. R. Acad. Sci. Paris, 272:433-436, 1971.
    • (1971) C. R. Acad. Sci. Paris , vol.272 , pp. 433-436
    • Michel, L.1
  • 89
    • 0003042599 scopus 로고    scopus 로고
    • Symmetry, invariants, topology. Basic tools
    • L. Michel and B. I. Zhilinskii. Symmetry, invariants, topology. Basic tools. Physics Reports, 341:11-84, 2001.
    • (2001) Physics Reports , vol.341 , pp. 11-84
    • Michel, L.1    Zhilinskii, B.I.2
  • 90
    • 0004190360 scopus 로고
    • Princetion University Press
    • J. W. Milnor. Morse Theory. Princetion University Press, 1969.
    • (1969) Morse Theory
    • Milnor, J.W.1
  • 91
    • 0346832843 scopus 로고
    • Caustics in time-reversible Hamiltonian systems
    • Singularity theory and its applications, Springer-Verlag
    • J. Montaldi. Caustics in time-reversible Hamiltonian systems. In Singularity theory and its applications, volume 1463 of Lecture Notes in Mathematics, pages 266-277. Springer-Verlag, 1991.
    • (1991) Lecture Notes in Mathematics , vol.1463 , pp. 266-277
    • Montaldi, J.1
  • 93
  • 94
    • 29444458091 scopus 로고
    • Existence of nonlinear normal modes of symmetric Hamiltonian systems
    • J. Montaldi, M. Roberts, and I. Stewart. Existence of nonlinear normal modes of symmetric Hamiltonian systems. Nonlinearity, 3:695-730, 1990.
    • (1990) Nonlinearity , vol.3 , pp. 695-730
    • Montaldi, J.1    Roberts, M.2    Stewart, I.3
  • 96
    • 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 Math.-Phys. Kl., 11:1-20, 1962.
    • (1962) Nachr. Akad. Wiss. Göttingen Math.-phys. Kl. , vol.11 , pp. 1-20
    • Moser, J.1
  • 97
    • 33748945689 scopus 로고
    • Algebraic Geometry. I Complex Protective Varieties, Springer Verlag. Berlin
    • D. Mumford. Algebraic Geometry. I Complex Protective Varieties, volume 221 of Grundlehren. Springer Verlag. Berlin, 1976.
    • (1976) Grundlehren. , vol.221
    • Mumford, D.1
  • 98
    • 0000234399 scopus 로고
    • Action-angle variables and their generalizations
    • N. N. Nekhoroshev. Action-angle variables and their generalizations. Trans. Moscow Math. Soc., 26:180-198, 1972.
    • (1972) Trans. Moscow Math. Soc. , vol.26 , pp. 180-198
    • Nekhoroshev, N.N.1
  • 99
    • 84908024292 scopus 로고
    • An exponential estimate of the time of stability of nearly integrable hamiltonian systems
    • N. N. Nekhoroshev. An exponential estimate of the time of stability of nearly integrable hamiltonian systems. Russian Math. Surveys, 32(6):1-65, 1977.
    • (1977) Russian Math. Surveys , vol.32 , Issue.6 , pp. 1-65
    • Nekhoroshev, N.N.1
  • 103
  • 104
    • 33748930393 scopus 로고    scopus 로고
    • Momentum maps and Hamiltonian reduction, Birkhäuser-Verlag, Basel
    • J.-P. Ortega and T. S. Ratiu. Momentum maps and Hamiltonian reduction, volume 222 of Progress in Mathematics. Birkhäuser-Verlag, Basel, 2004.
    • (2004) Progress in Mathematics , vol.222
    • Ortega, J.-P.1    Ratiu, T.S.2
  • 105
    • 0000202347 scopus 로고    scopus 로고
    • A reduction scheme for phase spaces with almost Kähler symmetry
    • M. Otto. A reduction scheme for phase spaces with almost Kähler symmetry. J. Geom. Phys., 4:101-118, 1987.
    • J. Geom. Phys. , vol.4 , pp. 101-118
    • Otto, M.1
  • 107
    • 0041162590 scopus 로고
    • Quantum and semiclassical description of a triply degenerate anharmonic oscillator
    • C. W. Patterson. Quantum and semiclassical description of a triply degenerate anharmonic oscillator. J. Chem. Phys., 83:4618-4632. 1985.
    • (1985) J. Chem. Phys. , vol.83 , pp. 4618-4632
    • Patterson, C.W.1
  • 108
    • 0003451932 scopus 로고
    • ∞ en présence de symétrie, Springer-Verlag
    • ∞ en présence de symétrie, volume 510 of Lecture Notes in Mathematics. Springer-Verlag, 1976.
    • (1976) Lecture Notes in Mathematics , vol.510
    • Poènaru, V.1
  • 110
    • 77956941103 scopus 로고
    • A guide to the Hénon-Heiles Hamiltonian
    • S. N. Pnevmatikos, editor, New York, Elsevier
    • D. L. Rod and R. C. Churchill. A guide to the Hénon-Heiles Hamiltonian. in S. N. Pnevmatikos, editor, Singularities and Dynamical Systems, pages 385-395, New York, 1985. Elsevier.
    • (1985) Singularities and Dynamical Systems , pp. 385-395
    • Rod, D.L.1    Churchill, R.C.2
  • 111
    • 1642271341 scopus 로고    scopus 로고
    • Normal forms, geometry, and dynamics of atomic and molecular systems with symmetry
    • D. Bambusi, M. Cadoni, and G. Gaeta, editors, Singapore, . World Scientific
    • D. A. Sadovskií. Normal forms, geometry, and dynamics of atomic and molecular systems with symmetry. In D. Bambusi, M. Cadoni, and G. Gaeta, editors, Symmetry and Perturbation Theory (Proceedings of the international conference SPT2001), pages -. Singapore, 2001. World Scientific.
    • (2001) Symmetry and Perturbation Theory (Proceedings of the International Conference SPT2001)
    • Sadovskií, D.A.1
  • 112
    • 0000126392 scopus 로고
    • Group theoretical and topological analysis of localized vibration-rotation states
    • D. A. Sadovskií and B. I. Zhilinskií. Group theoretical and topological analysis of localized vibration-rotation states. Phys. Rev. A, 47:2653-2671, 1993.
    • (1993) Phys. Rev. A , vol.47 , pp. 2653-2671
    • Sadovskií, D.A.1    Zhilinskií, B.I.2
  • 113
    • 0000739702 scopus 로고    scopus 로고
    • Tuning the hydrogen atom in crossed fields between the Zeeman and Stark limits
    • D. A. Sadovskií and B. I. Zhilinskií. Tuning the hydrogen atom in crossed fields between the Zeeman and Stark limits. Phys. Rev. A, 57:2867-2884, 1998.
    • (1998) Phys. Rev. A , vol.57 , pp. 2867-2884
    • Sadovskií, D.A.1    Zhilinskií, B.I.2
  • 114
    • 0001739654 scopus 로고    scopus 로고
    • Collapse of the Zeeman structure of the hydrogen atom in an external electric field
    • D. A. Sadovskií, B. I. Zhilinskií, and L. Michel. Collapse of the Zeeman structure of the hydrogen atom in an external electric field. Phys. Rev. A, 53:4064-4067, 1996.
    • (1996) Phys. Rev. A , vol.53 , pp. 4064-4067
    • Sadovskií, D.A.1    Zhilinskií, B.I.2    Michel, L.3
  • 115
    • 0042805662 scopus 로고
    • Smooth functions invariant under the action of a compact Lie group
    • G. Schwarz. Smooth functions invariant under the action of a compact Lie group. Topology. 14:63-68, 1975.
    • (1975) Topology. , vol.14 , pp. 63-68
    • Schwarz, G.1
  • 116
    • 0001229672 scopus 로고
    • Stratified symplectic spaces and reduction
    • R. Sjamaar and E. Lerman. Stratified symplectic spaces and reduction. Ann. of Math., 134:375-422, 1991.
    • (1991) Ann. of Math. , vol.134 , pp. 375-422
    • Sjamaar, R.1    Lerman, E.2
  • 117
    • 22244441450 scopus 로고
    • Topology and mechanics, I
    • S. Smale. Topology and mechanics, I. Inventiones Mathematicae, 10:305-331, 1970.
    • (1970) Inventiones Mathematicae , vol.10 , pp. 305-331
    • Smale, S.1
  • 118
    • 22244456049 scopus 로고
    • Topology and mechanics, II
    • S. Smale. Topology and mechanics, II. Inventiones Mathematicae, 11:45-64, 1970.
    • (1970) Inventiones Mathematicae , vol.11 , pp. 45-64
    • Smale, S.1
  • 119
    • 0030530551 scopus 로고
    • Yang-Mills and Dirac fields in a bag: Constraints and reduction
    • J. Śniatyeki, G. Schwarz, and L. Bates. Yang-Mills and Dirac fields in a bag: constraints and reduction. Comm. Math. Phys., 176:95-115, 1995.
    • (1995) Comm. Math. Phys. , vol.176 , pp. 95-115
    • Śniatyeki, J.1    Schwarz, G.2    Bates, L.3
  • 120
    • 0000643655 scopus 로고
    • Reduction and quantization for singular momentum mappings
    • J. Śniatyeki and A. Weinstein. Reduction and quantization for singular momentum mappings. Lett. Math. Phys., 7:155-161, 1983.
    • (1983) Lett. Math. Phys. , vol.7 , pp. 155-161
    • Śniatyeki, J.1    Weinstein, A.2
  • 122
    • 84966235340 scopus 로고
    • Invariants of finite groups and their applications to combinatorics
    • R. Stanley. Invariants of finite groups and their applications to combinatorics. Bull. Am. Math. Soc., 1(3):475-511, 1979.
    • (1979) Bull. Am. Math. Soc. , vol.1 , Issue.3 , pp. 475-511
    • Stanley, R.1
  • 124
    • 0003451932 scopus 로고
    • The Hamiltonian Hopf bifurcation, Springer, New York
    • J. C. van der Meer. The Hamiltonian Hopf bifurcation, volume 1160 of Lecture Notes in Mathematics. Springer, New York, 1985.
    • (1985) Lecture Notes in Mathematics , vol.1160
    • Van Der Meer, J.C.1
  • 126
    • 0035934245 scopus 로고    scopus 로고
    • Ab initio global potential, dipole, adiabatic and relativistic correction surfaces for the HCN/HNC system
    • T. van Mourik, G. J. Harris, O. L. Polyansky, J. Tennyson, A. G. Császár, and P. J. Knowles. Ab initio global potential, dipole, adiabatic and relativistic correction surfaces for the HCN/HNC system. J. Chem. Phys., 115:3706-3718, 2001.
    • (2001) J. Chem. Phys. , vol.115 , pp. 3706-3718
    • Van Mourik, T.1    Harris, G.J.2    Polyansky, O.L.3    Tennyson, J.4    Császá r, A.G.5    Knowles, P.J.6
  • 127
    • 0037525498 scopus 로고    scopus 로고
    • Quantum monodromy in integrable systems
    • S. Vu Ngoc. Quantum monodromy in integrable systems. Comm. Math. Phys., 203:465-479, 1999.
    • (1999) Comm. Math. Phys. , vol.203 , pp. 465-479
    • Vu Ngoc, S.1
  • 128
    • 0038515348 scopus 로고    scopus 로고
    • Quantum monodromy in the two-centre problem
    • H. Waalkens, A. Junge, and H. R. Dullin. Quantum monodromy in the two-centre problem. J. Phys. A, 36:L307-L314, 2003.
    • (2003) J. Phys. A , vol.36
    • Waalkens, H.1    Junge, A.2    Dullin, H.R.3
  • 129
    • 0001459972 scopus 로고
    • Normal modes for nonlinear Hamiltonian systems
    • A. Weinstein. Normal modes for nonlinear Hamiltonian systems. Invent. Math., 20:47-57, 1973.
    • (1973) Invent. Math. , vol.20 , pp. 47-57
    • Weinstein, A.1
  • 131
    • 0001316020 scopus 로고
    • On an algebraic problem concerning the normal forms of linear dynamical systems
    • J. Williamson, On an algebraic problem concerning the normal forms of linear dynamical systems. Amer. J. Math., 58:141-163, 1936.
    • (1936) Amer. J. Math. , vol.58 , pp. 141-163
    • Williamson, J.1
  • 136
    • 0002986165 scopus 로고
    • Qualitative analysis of vibrational polyads: N mode case
    • B. I. Zhilinskií. Qualitative analysis of vibrational polyads: N mode case. Chem. Phys., 137:1-13, 1989.
    • (1989) Chem. Phys. , vol.137 , pp. 1-13
    • Zhilinskií, B.I.1
  • 138
    • 9344225119 scopus 로고    scopus 로고
    • A note on focus-focus singularities
    • N. T. Zung. A note on focus-focus singularities. Diff. Geom. and Appl., 7:123-130, 1997.
    • (1997) Diff. Geom. and Appl. , vol.7 , pp. 123-130
    • Zung, N.T.1


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