Perturbations of lower dimensional tori for Hamiltonian systems

Journal of Differential Equations

Volumn 152, Issue 1, 1999, Pages 1-29

  You, Jiangong ^a  

^a NANJING UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033540589     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1998.3515     Document Type: Article

References (25)

1. 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.
2. Bourgain J. On Melnikov's persistency problem. Math. Res. Lett. 4:1997;445-458.
3. Bruno A. D. Analytic form of differential equations. Trudy Moskov. Mat. Obshch. 25:1971.
4. Cheng C.-Q., Sun Y.-S. Existence of KAM tori in degenerate Hamiltonian systems. J. Differential Equations. 114:1994;288-335.
5. L. Chierchia, J. You, KAM tori for 1D nonlinear wave equations with periodic boundary conditions, 1998.
6. Craig W., Wayne C. E. Newton's method and periodic solutions of nonlinear wave equations. Commun. Pure Appl. Math. 46:1993;1409-1498.
7. Graff S. M. On the continuation of stable invariant tori for Hamiltonian systems. J. Differential Equations. 15:1974;1-69.
8. Eliasson L. H. Perturbations of stable invariant tori for Hamiltonian systems. Ann. Scuola Norm. Sup. Pisa. 15:1988;115-147.
9. Kuksin S. B. Nearly Integrable Infinite Dimensional Hamiltonian Systems. Lecture Notes in Math. 1556:1993;Springer-Verlag, Berlin.
10. Kuksin S. B., Pöschel J. Invariant cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation. Ann. of Math. 142:1995;149-179.
11. Lancaster P. Theory of Matrices. 1969;Academic Press, New York and London.
12. Melnikov V. K. On some cases of the conservation of conditionally periodic motions under a small change of the Hamiltonian function. Soviet Math. Dokl. 6:1965;1592-1596.
13. Moser J. Convergent series expansions for quasiperiodic motions. Math. Ann. 169:1967;136-176.
14. Parasyuk I. O. Coisotropic invariant tori of Hamiltonian systems in the quasiclassical theory of motion of a conduction electon. Ukrain. Math. J. 42:1990;308-312.
15. Pöschel J. On elliptic lower dimensional tori in Hamiltonian systems. Math. Z. 202:1989;559-608.
16. Pöschel J. A KAM-Theorem for some Nonlinear Partial Differential Equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 23:1996;119-148.
17. Pöschel J. Integrability of Hamiltonian systems on Cantor Sets. Comm. Pure Appl. Math. 25:1982;653-695.
18. H. Rüssmann, On twist Hamiltonians, talk on the Colloque International: Mécanique céleste et systemes hamiltonians, Marseille, 1990.
19. Wayne C. E. Periodic and quasi-periodic solutions for nonlinear wave equations via KAM theory. Comm. Math. Phys. 127:1990;479-528.
20. Whitney H. Analytical extension of differentiable functions defined on closed set. Trans. Amer. Math. Soc. 36:1934;63-89.
21. Xia Z. The existence of the invariant tori in the volume preserving diffeomorphism. Ergodic Theory Dynam. Systems. 12:1992;621-631.
22. Xu J., You J., Qiu Q. Invariant tori for nearly integrable Hamiltonian systems with degeneracy. Math. Z. 226:1997.
23. Yoccoz J.-C. Travaux de Herman sur les tores invariants. Sem. Bourbaki. 754:1991-1992;311-344.
24. You J. A KAM theorem for hyperbolic-type degenerate lower dimensional tori in Hamiltonian systems. Comm. Math. Phys. 192:1998;145-168.
25. Zehnder E. Generalized implicit function theorems with applications to some small divisor problem, I and II. Comm. Pure Appl. Math. 28:1975;91-140.