메뉴 건너뛰기




Volumn 16, Issue 3, 2006, Pages 635-655

On elliptic lower dimensional tori for gevrey-smooth hamiltonian systems under rüssmann's non-degeneracy condition

Author keywords

Gevrey smooth; Hamiltonian systems; KAM iteration; R ssmann's non degeneracy condition

Indexed keywords


EID: 33845807803     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2006.16.635     Document Type: Article
Times cited : (17)

References (26)
  • 1
    • 0002764805 scopus 로고
    • Proof of a theorem of A.N. Kolmogorov on the preservation of conditionally periodic motions under a small perturbation of the Hamiltonian
    • Arnold, V. I., Proof of a theorem of A.N. Kolmogorov on the preservation of conditionally periodic motions under a small perturbation of the Hamiltonian, Uspehi Math. Nauk 18 (1963), 13-40;
    • (1963) Uspehi Math. Nauk , vol.18 , pp. 13-40
    • Arnold, V.I.1
  • 3
    • 0031287692 scopus 로고    scopus 로고
    • On Melnikov's persistency problem
    • Bourgain, J., On Melnikov's persistency problem, Math. Res. Lett. 4 (4) (1997), 445-458.
    • (1997) Math. Res. Lett. , vol.4 , Issue.4 , pp. 445-458
    • Bourgain, J.1
  • 5
    • 0142137606 scopus 로고    scopus 로고
    • Normal-internal resonances in quasi-periodically forced oscillators: A conservative approach
    • Broer, H., Hanßmann, H., Jorba, A., Villanueva, J., Wagener, F., Normal-internal resonances in quasi-periodically forced oscillators: a conservative approach, Nonlinearity 16 (2003), 1751-1791.
    • (2003) Nonlinearity , vol.16 , pp. 1751-1791
    • Broer, H.1    Hanßmann, H.2    Jorba, A.3    Villanueva, J.4    Wagener, F.5
  • 6
    • 4544242704 scopus 로고    scopus 로고
    • Moser's theorem for lower dimensional tori
    • Chierchia, L., Qian, D., Moser's theorem for lower dimensional tori, J. Differential Equations 206 (2004), 55-93.
    • (2004) J. Differential Equations , vol.206 , pp. 55-93
    • Chierchia, L.1    Qian, D.2
  • 7
    • 0000412297 scopus 로고
    • Perturbations of stable invariant tori for Hamiltonian systems
    • Eliasson, L. H., Perturbations of stable invariant tori for Hamiltonian systems, Ann. Sc. Norm. Sup. Pisa 15 (1988), 115-147.
    • (1988) Ann. Sc. Norm. Sup. Pisa , vol.15 , pp. 115-147
    • Eliasson, L.H.1
  • 8
    • 0001246972 scopus 로고
    • On conservation of conditionally periodic motions for a small change in Hamilton's function
    • Russian
    • Kolmogorov, A. N., On conservation of conditionally periodic motions for a small change in Hamilton's function, Dokl. Akad. Nauk SSSR 98 (1954), 525-530 (Russian).
    • (1954) Dokl. Akad. Nauk SSSR , vol.98 , pp. 525-530
    • Kolmogorov, A.N.1
  • 9
    • 0011535486 scopus 로고
    • Perturbation theory of conditionally periodic solutions of infinite-dimensional Hamiltonian systems and its applications to the Korteweg-de Vries equation
    • 431 (Russian)
    • Kuksin, S. B., Perturbation theory of conditionally periodic solutions of infinite-dimensional Hamiltonian systems and its applications to the Korteweg-de Vries equation, Mat. Sb. (N. S.) 136 (178) (3) (1988), 396-412, 431 (Russian).
    • (1988) Mat. Sb. (N. S.) , vol.136 , Issue.3-178 , pp. 396-412
    • Kuksin, S.B.1
  • 10
  • 11
    • 3042570326 scopus 로고
    • Convergent series expansions for quasi-periodic motions
    • Moser, J., Convergent series expansions for quasi-periodic motions, Math. Ann. 169 (1967), 136-176.
    • (1967) Math. Ann. , vol.169 , pp. 136-176
    • Moser, J.1
  • 12
    • 0039034734 scopus 로고
    • On certain cases of conservation of almost periodic motions with a small change of the Hamiltonian function
    • Russian
    • Melnikov, V. K., On certain cases of conservation of almost periodic motions with a small change of the Hamiltonian function, Dokl. Akad. Nauk SSSR 165 (1965), 1245-1248 (Russian).
    • (1965) Dokl. Akad. Nauk SSSR , vol.165 , pp. 1245-1248
    • Melnikov, V.K.1
  • 13
    • 84990623105 scopus 로고
    • Integrability of Hamiltonian systems on Cantor sets
    • Pöschel, J., Integrability of Hamiltonian systems on Cantor sets, Comm. Pure Appl. Math. 35 (1982), 653-696.
    • (1982) Comm. Pure Appl. Math. , vol.35 , pp. 653-696
    • Pöschel, J.1
  • 14
    • 0000882204 scopus 로고
    • On elliptic lower dimensional tori in Hamiltonian systems
    • Pöschel, J., On elliptic lower dimensional tori in Hamiltonian systems, Math. Z. 202(4) (1989), 559-608.
    • (1989) Math. Z. , vol.202 , Issue.4 , pp. 559-608
    • Pöschel, J.1
  • 16
    • 85129605434 scopus 로고    scopus 로고
    • A KAM-theorem for some nonlinear PDEs
    • Pöschel, J., A KAM-theorem for some nonlinear PDEs, Ann. Sc. Norm. Sup. Pisa 23 (1996), 119-148.
    • (1996) Ann. Sc. Norm. Sup. Pisa , vol.23 , pp. 119-148
    • Pöschel, J.1
  • 17
    • 0034347241 scopus 로고    scopus 로고
    • Invariant tori, effective stability, and quasimodes with exponentially small error terms. I. Birkhoff normal forms
    • Popov, G., Invariant tori, effective stability, and quasimodes with exponentially small error terms. I. Birkhoff normal forms, Ann. Henri Poincaré 1(2) (2000), 223-248.
    • (2000) Ann. Henri Poincaré , vol.1 , Issue.2 , pp. 223-248
    • Popov, G.1
  • 18
    • 9344247432 scopus 로고    scopus 로고
    • KAM theorem for Gevrey Hamiltonians
    • Popov, G., KAM theorem for Gevrey Hamiltonians, Ergodic Theory Dynam. Systems 24 (2004), 1753-1786.
    • (2004) Ergodic Theory Dynam. Systems , vol.24 , pp. 1753-1786
    • Popov, G.1
  • 19
    • 51249166750 scopus 로고
    • On the Lebesgue measure of the periodic points of a contact manifold
    • Petkov, V. and Popov, G., On the Lebesgue measure of the periodic points of a contact manifold, Math. Z. 218 (1995), No. 1, 91-102.
    • (1995) Math. Z. , vol.218 , Issue.1 , pp. 91-102
    • Petkov, V.1    Popov, G.2
  • 20
    • 0000285454 scopus 로고    scopus 로고
    • Invariant tori in non-degenerate nearly integrable Hamiltonian systems
    • Rüssmann, H., Invariant tori in non-degenerate nearly integrable Hamiltonian systems, Regul. Chaotic Dynamics 6 (2) (2001), 119-204.
    • (2001) Regul. Chaotic Dynamics , vol.6 , Issue.2 , pp. 119-204
    • Rüssmann, H.1
  • 21
    • 0042031279 scopus 로고    scopus 로고
    • A note on Gevrey regular KAM theory and the inverse approximation lemma
    • Wagener, F., A note on Gevrey regular KAM theory and the inverse approximation lemma, Dyn. Syst. 18 (2003), 159-163.
    • (2003) Dyn. Syst. , vol.18 , pp. 159-163
    • Wagener, F.1
  • 22
    • 77956456169 scopus 로고
    • Analytic extensions of differentiable functions defined in closed sets
    • Whitney, H., Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc. 36 (1934), 63-89.
    • (1934) Trans. Amer. Math. Soc. , vol.36 , pp. 63-89
    • Whitney, H.1
  • 23
    • 0035604021 scopus 로고    scopus 로고
    • Persistence of lower-dimensional tori under the first Melnikov's nonresonance condition
    • Xu, J., You, J., Persistence of lower-dimensional tori under the first Melnikov's nonresonance condition, J. Math. Pures Appl. (9) 80 (10) (2001), 1045-1067.
    • (2001) J. Math. Pures Appl. (9) , vol.80 , Issue.10 , pp. 1045-1067
    • Xu, J.1    You, J.2
  • 24
    • 0031285618 scopus 로고    scopus 로고
    • Invariant tori of nearly integrable Hamiltonian systems with degeneracy
    • Xu, J., You, J., Qiu, Q., Invariant tori of 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
  • 26
    • 0033540589 scopus 로고    scopus 로고
    • Perturbations of lower dimensional tori for Hamiltonian systems
    • You, J., Perturbations of lower dimensional tori for Hamiltonian systems, J. Differential Equations 152 (1999), 1-29.
    • (1999) J. Differential Equations , vol.152 , pp. 1-29
    • You, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.