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Volumn 10, Issue 1, 2000, Pages 49-68

KAM-type theorem on resonant surfaces for nearly integrable Hamiltonian systems

Author keywords

Hamiltonian systems; KAM type theorem; Resonant invariant tori

Indexed keywords


EID: 0006689355     PISSN: 09388974     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003329910003     Document Type: Article
Times cited : (35)

References (20)
  • 1
    • 0002764803 scopus 로고
    • Proof of A. N. Kolmogorov's theorem on the preservation of quasi periodic motions under small perturbations of the Hamiltonian
    • V. I. Arnold, Proof of A. N. Kolmogorov's theorem on the preservation of quasi periodic motions under small perturbations of the Hamiltonian, Usp. Math. USSR 18 (1963), 13-40.
    • (1963) Usp. Math. USSR , vol.18 , pp. 13-40
    • Arnold, V.I.1
  • 2
    • 84963026889 scopus 로고
    • Construction of quasi-periodic solution for Hamiltonian perturbations of linear equations and applications to nonlinear PDE
    • J. Bourgain, Construction of quasi-periodic solution for Hamiltonian perturbations of linear equations and applications to nonlinear PDE, Int. Math. Res. Not. 11 (1994), 475-497.
    • (1994) Int. Math. Res. Not. , vol.11 , pp. 475-497
    • Bourgain, J.1
  • 3
    • 0003210170 scopus 로고    scopus 로고
    • Quasi-periodic motions in families of dynamical systems
    • Springer-Verlag, New York
    • H. Broer, G. Huitema, and M. Sevryuk, Quasi-Periodic Motions in Families of Dynamical Systems, Lecture Notes in Math., 1645, Springer-Verlag, New York, 1996.
    • (1996) Lecture Notes in Math. , vol.1645
    • Broer, H.1    Huitema, G.2    Sevryuk, M.3
  • 4
    • 0040799578 scopus 로고    scopus 로고
    • Birkhoff-Kolmogorov-Arnold-Moser tori in convex Hamiltonian systems
    • C.-Q. Cheng, Birkhoff-Kolmogorov-Arnold-Moser tori in convex Hamiltonian systems, Commun. Math. Phys. 177 (1996), 529-559.
    • (1996) Commun. Math. Phys. , vol.177 , pp. 529-559
    • Cheng, C.-Q.1
  • 6
    • 0002445576 scopus 로고
    • Biasymptotic solutions of perturbed integrable Hamiltonian systems
    • L. H. Eliasson, Biasymptotic solutions of perturbed integrable Hamiltonian systems, Bol. Soc. Mat. 25 (1994), 57-76.
    • (1994) Bol. Soc. Mat. , vol.25 , pp. 57-76
    • Eliasson, L.H.1
  • 7
    • 0003053373 scopus 로고
    • On the continuation of hyperbolic invariant tori for Hamiltonian systems
    • S. M. Graff, On the continuation of hyperbolic invariant tori for Hamiltonian systems, J. Diff. Eq. 15 (1974), 1-60.
    • (1974) J. Diff. Eq. , vol.15 , pp. 1-60
    • Graff, S.M.1
  • 8
    • 0001246972 scopus 로고
    • On quasi-periodic motions under small perturbations of the Hamiltonian
    • A. N. Kolmogorov, On quasi-periodic motions under small perturbations of the Hamiltonian, Dokl. Akad. Nauk USSR 98 (1954), 527-530.
    • (1954) Dokl. Akad. Nauk USSR , vol.98 , pp. 527-530
    • Kolmogorov, A.N.1
  • 9
    • 0004190360 scopus 로고
    • Princeton University Press, Princeton, NJ
    • J. Milnor, Morse Theory, Princeton University Press, Princeton, NJ, 1963.
    • (1963) Morse Theory
    • Milnor, J.1
  • 10
    • 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. Gott. Math. Phys. K1, 2 (1962), 1-20.
    • (1962) Nachr. Akad. Wiss. Gott. Math. Phys. K1 , vol.2 , pp. 1-20
    • Moser, J.1
  • 13
    • 0003909276 scopus 로고
    • AIP Press, Williston, MD
    • H. Poincaré, Les Méthodes Nouvelles de la Mécaniques Céleste, I-III, Dover Publications, New York, 1957; English translation: New Methods of Celestial Mechanics, AIP Press, Williston, MD, 1992.
    • (1992) New Methods of Celestial Mechanics
  • 14
    • 84990623105 scopus 로고
    • Integrability of Hamiltonian systems on Cantor sets
    • J. Pöschel, Integrability of Hamiltonian systems on Cantor sets, Commun. Pure Appl. Math. 35 (1982), 653-696.
    • (1982) Commun. Pure Appl. Math. , vol.35 , pp. 653-696
    • Pöschel, J.1
  • 15
    • 0000882204 scopus 로고
    • On the elliptic lower dimensional tori in Hamiltonian systems
    • J. Pöschel, On the elliptic lower dimensional tori in Hamiltonian systems, Math. Z. 202 (1989), 559-608.
    • (1989) Math. Z. , vol.202 , pp. 559-608
    • Pöschel, J.1
  • 16
    • 0000770795 scopus 로고    scopus 로고
    • KAM theory near multiplicity one resonant surfaces in perturbations of A-priori stable Hamiltonian systems
    • M. Rudnev and S. Wiggins, KAM theory near multiplicity one resonant surfaces in perturbations of A-priori stable Hamiltonian systems, J. Nonlin. Sci. 7 (1997), 177-209.
    • (1997) J. Nonlin. Sci. , vol.7 , pp. 177-209
    • Rudnev, M.1    Wiggins, S.2
  • 17
    • 0000764886 scopus 로고
    • Mechanism for destroying resonance tori of Hamiltonian systems
    • D. V. Treshchev, Mechanism for destroying resonance tori of Hamiltonian systems, Mat. USSR Sb. 180 (1989), 1325-1346.
    • (1989) Mat. USSR Sb. , vol.180 , pp. 1325-1346
    • Treshchev, D.V.1
  • 19
    • 0031285618 scopus 로고    scopus 로고
    • Invariant tori for nearly integrable Hamiltonian systems with degeneracy
    • J. Xu, J. You, and Q. Qiu, Invariant tori for nearly integrable Hamiltonian systems with degeneracy, Math. Z. 226 (1997), 375-387.
    • (1997) Math. Z. , vol.226 , pp. 375-387
    • Xu, J.1    You, J.2    Qiu, Q.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.