On Invariant Tori of Nearly Integrable Hamiltonian Systems with Quasiperiodic Perturbation

Fixexd point theory and applications

Rong Cheng¹  Dongfeng Zhang² 

[1] College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing, China;Department of Mathematics, Southeast University, Nanjing, China

关键词: Hamiltonian System;    Invariant Torus;    Invariant Curve;    Integrable Hamiltonian System;    Nondegeneracy Condition;   

DOI  :  10.1155/2010/697343

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We are concerned with the persistence of frequency of invariant tori for analytic integrable Hamiltonian system with quasiperiodic perturbation. It is proved that if the unperturbed system satisfies the Rüssmann's nondegeneracy condition and has nonzero Brouwer's topological degree at some Diophantine frequency; the perturbed system satisfies the colinked nonresonant condition, then the invariant torus with this frequency persists under quasiperiodic perturbation.

【 授权许可】

CC BY