Persistence of lower-dimensional tori under the first Melnikov's non-resonance condition

Journal des Mathematiques Pures et Appliquees

Volumn 80, Issue 10, 2001, Pages 1045-1067

  Xu, Junxiang ^a   You, Jiangong ^b  

^a SOUTHEAST UNIVERSITY   (China)

^b NANJING UNIVERSITY   (China)

Author keywords

Hamiltonian systems; Invariant tori; KAM iteration; Small divisor conditions

Indexed keywords

EID: 0035604021     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-7824(01)01221-1     Document Type: Article

References (19)

1. Arnold V.I. Dynamical Systems. Encyclopaedia of Mathematical Sciences. 3:1988;Sringer-Verlag.
2. Bourgain J. Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE. Internat. Math. Res. Notices. 1994;475-497.
3. Bourgain J. On Melnikov's persistency problem. Math. Res. Lett. 4:1997;445-458.
4. Craig W., Wayne C.E. Newton's method periodic solutions of nonlinear wave equations. Comm. Pure Appl. Math. 46:1993;1409-1498.
5. Eliasson L.H. Perturbations of stable invariant tori for Hamiltonian systems. Ann. Sci. Norm. Superior Pisa. 15:1988;115-147.
6. Kuksin S.B. Perturbation theory for quasiperiodic solutions of infinite dimensional Hamiltonian systems, and its applications to the Korteweg-de Vries equations. Mat. Sb. 136 (178):(3):1988;. English transl. in Math. USSR Sb. 64 (1989) 397-417.
7. Kuksin S.B. Perturbation theory for quasiperiodic solutions of infinite dimensional Hamiltonian systems, and its applications to the Korteweg-de Vries equations. Mat. Sb. 136 (178):(3):1988;. English transl. in Math. USSR Sb. 64 (1989) 397-417.
8. Kuksin S.B. Nearly Integrable Infinite Dimensional Hamiltonian Systems. Lecture Notes in Math. 1556:1993;Springer, Berlin.
9. Melnikov V.K. On some cases of conservation of conditionally periodic motions under a small change of the Hamiltonian function. Soviet Math. Dokl. 6:1965;1592-1596.
10. Melnikov V.K. A family of conditionally periodic solutions of a Hamiltonian systems. Soviet Math. Dokl. 9:1968;882-886.
11. Pöschel J. On elliptic lower dimensional tori in Hamiltonian systems. Math. Z. 202:(4):1989;559-608.
12. Pöschel J. A KAM-theorem for some nonlinear partial differential equations. Ann. Scuola. Norm. Sup. Pisa Cl. Sci. 23:1996;119-148.
13. H. RUSSMANN, On twist Hamiltonian, Talk on the Colloque International: Mécanique Céleste et Systèmes Hamiltoniens, Marseille, 1990.
14. Sevryuk M.B. KAM-stable Hamiltonians. J. Dynamics Control Systems. 1:1995;351-366.
15. Whitney H. Analytical extensions of differentiable functions defined in closed sets. Trans. Amer. Math. Soc. 36:1934;63-89.
16. Xu J. Perturbations of elliptic lower dimensional tori for small perturbation of degenerate integrable Hamiltonian systems. J. Math. Anal. Appl. 208:1997;372-387.
17. J. XU, J. YOU, A sympelctic map and its application to persistence of lower dimensional tori, Preprint, 1999.
18. Xu J., You J., Qiu Q. Invariant tori of nearly integrable Hamiltonian systems with degeneracy. Math. Z. 226:1997;375-386.
19. You J. Perturbations of lower dimensional tori for Hamiltonian systems. J. Differential Equations. 152:1999;1-29.