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Volumn 32, Issue 2, 1999, Pages 131-159

A Dirichlet criterion for the stability of periodic and relative periodic orbits in Hamiltonian systems

Author keywords

Dirichlet criterion; Hamiltonian systems; Periodic and relative periodic orbits; Stability

Indexed keywords


EID: 0033472562     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0393-0440(99)00025-X     Document Type: Article
Times cited : (4)

References (52)
  • 3
    • 0002764803 scopus 로고
    • Proof of A. N. Kolmogorov's theorem on the perturbation of quasi-periodic motions under small perturbations of the Hamiltonian
    • Russian
    • V.I. Arnold, Proof of A. N. Kolmogorov's theorem on the perturbation of quasi-periodic motions under small perturbations of the Hamiltonian, (Russian) Usp. Mat. Nauk SSSR 18 (1963) 13-40; [(English) Russian Math. Surveys 18 (1963) 9-36].
    • (1963) Usp. Mat. Nauk SSSR , vol.18 , pp. 13-40
    • Arnold, V.I.1
  • 4
    • 0002764805 scopus 로고
    • English
    • V.I. Arnold, Proof of A. N. Kolmogorov's theorem on the perturbation of quasi-periodic motions under small perturbations of the Hamiltonian, (Russian) Usp. Mat. Nauk SSSR 18 (1963) 13-40; [(English) Russian Math. Surveys 18 (1963) 9-36].
    • (1963) Russian Math. Surveys , vol.18 , pp. 9-36
  • 5
    • 0002771146 scopus 로고
    • On an a priori estimate in the theory of hydrodynamical stability
    • Russian
    • V.I. Arnold, On an a priori estimate in the theory of hydrodynamical stability, (Russian) Izv. Vyssh. Uchebn. Zaved. Mat. Nauk 54 (1966) 3-5 [(English) Amer. Math. Soc. Transl. 79 (1969) 267-269].
    • (1966) Izv. Vyssh. Uchebn. Zaved. Mat. Nauk , vol.54 , pp. 3-5
    • Arnold, V.I.1
  • 6
    • 0000945983 scopus 로고
    • English
    • V.I. Arnold, On an a priori estimate in the theory of hydrodynamical stability, (Russian) Izv. Vyssh. Uchebn. Zaved. Mat. Nauk 54 (1966) 3-5 [(English) Amer. Math. Soc. Transl. 79 (1969) 267-269].
    • (1969) Amer. Math. Soc. Transl. , vol.79 , pp. 267-269
  • 9
    • 0001541212 scopus 로고    scopus 로고
    • Proper group actions and symplectic stratified spaces
    • L. Bates, E. Lerman, Proper group actions and symplectic stratified spaces, Pacific J. Math. 181 (2) (1997) 201-229.
    • (1997) Pacific J. Math. , vol.181 , Issue.2 , pp. 201-229
    • Bates, L.1    Lerman, E.2
  • 10
    • 0039117989 scopus 로고    scopus 로고
    • Fast rotations of the rigid body: A study by Hamiltonian perturbation theory, Part I
    • G. Benettin, F. Fassò, Fast rotations of the rigid body: A study by Hamiltonian perturbation theory, Part I, Nonlinearity 9 (1996) 137-186.
    • (1996) Nonlinearity , vol.9 , pp. 137-186
    • Benettin, G.1    Fassò, F.2
  • 11
    • 0000644189 scopus 로고    scopus 로고
    • Fast rotations of the rigid body: A study by Hamiltonian perturbation theory
    • G. Benettin, F. Fassò, M. Guzzo, Fast rotations of the rigid body: A study by Hamiltonian perturbation theory, Part II: Gyroscopic Rotations, Nonlinearity 10 (1997) 1695-1717.
    • (1997) Part II: Gyroscopic Rotations, Nonlinearity , vol.10 , pp. 1695-1717
    • Benettin, G.1    Fassò, F.2    Guzzo, M.3
  • 13
    • 0003323455 scopus 로고
    • Differentiable manifolds
    • Van Nostrand Reinhold
    • F. Brickell R.S. Clark, Differentiable manifolds, An Introduction, Van Nostrand Reinhold, 1970.
    • (1970) An Introduction
    • Brickell, F.1    Clark, R.S.2
  • 16
    • 0032187844 scopus 로고    scopus 로고
    • Nekhoroshev-stability of elliptic equilibria of Hamiltonian systems
    • F. Fassò, M. Guzzo, G. Benettin, Nekhoroshev-stability of elliptic equilibria of Hamiltonian systems, Commun. Math. Phys. 197 (1998) 347-360.
    • (1998) Commun. Math. Phys. , vol.197 , pp. 347-360
    • Fassò, F.1    Guzzo, M.2    Benettin, G.3
  • 17
    • 0000163515 scopus 로고
    • Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem
    • A. Giorgilli, A. Delshams, E. Fontich, L. Galgani, C. Simó, Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem, J. Differential Equations 77 (1989) 167-198.
    • (1989) J. Differential Equations , vol.77 , pp. 167-198
    • Giorgilli, A.1    Delshams, A.2    Fontich, E.3    Galgani, L.4    Simó, C.5
  • 19
    • 0000618323 scopus 로고
    • A normal form for the moment map
    • S. Sternberg (Ed.), Differential Geometric Methods in Mathematical Physics, D. Reidel Publishing Company
    • V. Guillemin, S. Sternberg, A normal form for the moment map, in: S. Sternberg (Ed.), Differential Geometric Methods in Mathematical Physics, Mathematical Physics Studies, vol. 6, D. Reidel Publishing Company, 1984.
    • (1984) Mathematical Physics Studies , vol.6
    • Guillemin, V.1    Sternberg, S.2
  • 22
    • 0002245635 scopus 로고
    • Nonlinear stability of fluid and plasma equilibria
    • D. Holm, J.E. Marsden, T.S. Ratiu, A. Weinstein, Nonlinear stability of fluid and plasma equilibria, Phys. Rep. 123 (1985) 1-116.
    • (1985) Phys. Rep. , vol.123 , pp. 1-116
    • Holm, D.1    Marsden, J.E.2    Ratiu, T.S.3    Weinstein, A.4
  • 23
    • 0009085273 scopus 로고
    • Invariant tori and cylinders for a class of perturbed Hamiltonian systems
    • T.S. Ratiu (Ed.), Springer, Berlin
    • E.A. Lacomba, J. Llibre, A. Nunes, Invariant tori and cylinders for a class of perturbed Hamiltonian systems, in: T.S. Ratiu (Ed.), The Geometry of Hamiltonian Systems, Springer, Berlin, 1991, pp. 373-385.
    • (1991) The Geometry of Hamiltonian Systems , pp. 373-385
    • Lacomba, E.A.1    Llibre, J.2    Nunes, A.3
  • 26
    • 0009267657 scopus 로고    scopus 로고
    • Stability and persistence of relative equilibria at singular values of the moment map
    • E. Lerman, S.F. Singer, Stability and persistence of relative equilibria at singular values of the moment map, Nonlinearity 11 (1998) 1637-1649.
    • (1998) Nonlinearity , vol.11 , pp. 1637-1649
    • Lerman, E.1    Singer, S.F.2
  • 29
    • 0025897929 scopus 로고
    • On the stability of relative equilibria
    • J. Maddocks, On the stability of relative equilibria, IMA J. Appl. Math. 46 (1991) 71-99.
    • (1991) IMA J. Appl. Math. , vol.46 , pp. 71-99
    • Maddocks, J.1
  • 30
    • 0001620007 scopus 로고
    • La gravitation et le principe de l'égalité de l'action et de la réaction
    • G. Maneff, La gravitation et le principe de l'égalité de l'action et de la réaction, Comp. Rend. 178 (1924) 2159-2161.
    • (1924) Comp. Rend. , vol.178 , pp. 2159-2161
    • Maneff, G.1
  • 31
    • 0001643805 scopus 로고
    • Die gravitation und das prinzip von wirkung und gegenwirkung
    • G. Maneff, Die gravitation und das prinzip von wirkung und gegenwirkung, Zeit. Phys. 31 (1925) 786-802.
    • (1925) Zeit. Phys. , vol.31 , pp. 786-802
    • Maneff, G.1
  • 32
    • 0000104340 scopus 로고
    • Le principe de la moindre action et la gravitation
    • G. Maneff, Le principe de la moindre action et la gravitation, Comp. Rend. 190 (1930) 963-965.
    • (1930) Comp. Rend. , vol.190 , pp. 963-965
    • Maneff, G.1
  • 33
    • 0000189873 scopus 로고
    • La gravitation et l'énergie au zéro
    • G. Maneff, La gravitation et l'énergie au zéro, Comp. Rend. 190 (1930) 1374-1377.
    • (1930) Comp. Rend. , vol.190 , pp. 1374-1377
    • Maneff, G.1
  • 34
    • 0001307473 scopus 로고
    • Modéle d'action hamiltonienne d'un groupe the lie sur une variété symplectique
    • C.-M. Marle, Modéle d'action hamiltonienne d'un groupe the lie sur une variété symplectique, Rend. Sem. Mat. Univers. Politecn. Torino 43 (2) (1985) 227-251.
    • (1985) Rend. Sem. Mat. Univers. Politecn. Torino , vol.43 , Issue.2 , pp. 227-251
    • Marle, C.-M.1
  • 35
    • 0003274786 scopus 로고    scopus 로고
    • Introduction to mechanics and symmetry
    • Springer, Berlin
    • J.E. Marsden, T.S. Ratiu, Introduction to mechanics and symmetry, Texts in Applied Mathematics, vol. 17, Springer, Berlin, 1994.
    • Texts in Applied Mathematics , vol.17 , pp. 1994
    • Marsden, J.E.1    Ratiu, T.S.2
  • 36
    • 49549151837 scopus 로고
    • Reduction of symplectic manifolds with symmetry
    • J.E. Marsden, A. Weinstein, Reduction of symplectic manifolds with symmetry, Rep. Math. Phys. 5 (1) (1974) 121-130.
    • (1974) Rep. Math. Phys. , vol.5 , Issue.1 , pp. 121-130
    • Marsden, J.E.1    Weinstein, A.2
  • 37
    • 0003252211 scopus 로고    scopus 로고
    • Morse theory
    • Princeton University Press, NJ
    • J. Milnor, Morse theory, Studies, vol. 51, Princeton University Press, NJ, 1969.
    • Studies , vol.51 , pp. 1969
    • Milnor, J.1
  • 38
    • 0001463128 scopus 로고    scopus 로고
    • Persistence and stability of relative equilibria
    • J. Montaldi, Persistence and stability of relative equilibria, Nonlinearity 10 (1997) 449-466.
    • (1997) Nonlinearity , vol.10 , pp. 449-466
    • Montaldi, J.1
  • 40
    • 84980072725 scopus 로고
    • New aspects in the theory of stability of Hamiltonian systems
    • J. Moser, New aspects in the theory of stability of Hamiltonian systems, Comm. Pure Appl. Math. 11 (1958) 81-114.
    • (1958) Comm. Pure Appl. Math. , vol.11 , pp. 81-114
    • Moser, J.1
  • 41
    • 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) (1977) 1-65 [Uspekhi Mat. Nauk 32 (6) (1977) 5-66].
    • (1977) Russian Math. Surveys , vol.32 , Issue.6 , pp. 1-65
    • Nekhoroshev, N.N.1
  • 42
    • 84908024292 scopus 로고
    • N.N. Nekhoroshev, An exponential estimate of the time of stability of nearly-integrable Hamiltonian systems, Russian Math. Surveys 32 (6) (1977) 1-65 [Uspekhi Mat. Nauk 32 (6) (1977) 5-66].
    • (1977) Uspekhi Mat. Nauk , vol.32 , Issue.6 , pp. 5-66
  • 43
    • 0008993661 scopus 로고
    • A stability criterion for Hamiltonian systems with symmetry
    • Y.-G. Oh, A stability criterion for Hamiltonian systems with symmetry, J. Geom. Phys. 4 (2) (1987) 163-182.
    • (1987) J. Geom. Phys. , vol.4 , Issue.2 , pp. 163-182
    • Oh, Y.-G.1
  • 45
    • 0033130424 scopus 로고    scopus 로고
    • Stability of Hamiltonian relative equilibria
    • J.-P. Ortega, T.S. Ratiu, Stability of Hamiltonian relative equilibria, Nonlinearity 12 (1999) 693-720.
    • (1999) Nonlinearity , vol.12 , pp. 693-720
    • Ortega, J.-P.1    Ratiu, T.S.2
  • 46
    • 0001719339 scopus 로고
    • Relative equilibria in Hamiltonian systems: The dynamic interpretation of nonlinear stability on a reduced phase space
    • G.W. Patrick, Relative equilibria in Hamiltonian systems: The dynamic interpretation of nonlinear stability on a reduced phase space, J. Geom. Phys. 9 (1992) 111-119.
    • (1992) J. Geom. Phys. , vol.9 , pp. 111-119
    • Patrick, G.W.1
  • 47
    • 0001703398 scopus 로고
    • The closing lemma
    • C. Pugh, The closing lemma, Amer. J. Math. 89 (1967) 956-1009.
    • (1967) Amer. J. Math. , vol.89 , pp. 956-1009
    • Pugh, C.1
  • 48
    • 0001551716 scopus 로고
    • An improved closing lemma and a general density theorem
    • C. Pugh, An improved closing lemma and a general density theorem, Amer. J. Math. 89 (1967) 1010-1021.
    • (1967) Amer. J. Math. , vol.89 , pp. 1010-1021
    • Pugh, C.1
  • 49
    • 0000631525 scopus 로고
    • Generic properties of conservative systems
    • R.C. Robinson, Generic properties of conservative systems, Amer. J. Math 92 (1970) 562-603.
    • (1970) Amer. J. Math , vol.92 , pp. 562-603
    • Robinson, R.C.1
  • 50
    • 0002985376 scopus 로고
    • Stability of relative equilibria, Part I: The reduced energy-momentum method
    • J.C. Simo, D. Lewis, J.E. Marsden, Stability of relative equilibria, Part I: The reduced energy-momentum method, Arch. Rational Mech. Anal. 115 (1991) 15-59.
    • (1991) Arch. Rational Mech. Anal. , vol.115 , pp. 15-59
    • Simo, J.C.1    Lewis, D.2    Marsden, J.E.3
  • 51
    • 0001229672 scopus 로고
    • Stratified symplectic spaces and reduction
    • R. Sjamaar, E. Lerman, Stratified symplectic spaces and reduction, Ann. of Math. 134 (1991) 375-422.
    • (1991) Ann. of Math. , vol.134 , pp. 375-422
    • Sjamaar, R.1    Lerman, E.2


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