退化情形下高余维双曲不变环面的存在性
摘要
给出了近可积Hamilton系统共振区内的余维2低维不变环面在某种非完全退化情形下的存在性.
出处
《中国科学(A辑)》
CSCD
北大核心
2002年第7期640-649,共10页
Science in China(Series A)
基金
国家重点基础研究发展规划资助项目(批准号:G2000077303)
参考文献16
-
1[1]Arnol'd V I. Proof of a theorem of A N Kolmogorov on the invariance of quasi-periodic motions under small perturbation of the Hamiltonian. Usp Math USSR, 1963, 18:9~36
-
2[2]Craig W, Wayne C E. Newton's method and periodic solutions of nonlinear wave equations. Commun Pure Appl Math, 1993, 46:1409~1498
-
3[3]Eliasson L H. Perturbations of stable invariant tori for Hamiltonian systems. Ann sc Norm Sup Psia, 1988,15:115~147
-
4[4]Graff S M. On the continuation of stable invariant tori for Hamiltonian systems. J Differ Eqs, 1974, 15:1~69
-
5[5]Kuksin S B. Nearly Intergrable Infinite Dimensional Hamiltonian Systems. Lect Notes in Math, Vol 1556.Berlin: Springer, 1993
-
6[6]Moser J. Convergent series expansions for quasiperiodic motions. Math Ann, 1967, 169(1): 136~176
-
7[7]Takens F. Singularities of vector fields. Publ Math I H E S, 1974, 43:479~528
-
8[8]Zehnder E. Generalized implicit function theorems with applications to some small divisor problem, I. Commun Pure Appl Math, 1975, 28:91~140
-
9[9]Zehnder E. Generalized implicit function theorems with applications to some small divisor problem, II.Commun Pure Appl math, 1976, 29:49~111
-
10[10]Bernstein D, Katok A. Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian systems with convex Hamiltonian. Invent Math, 1987, 88:225~241