Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 697343, 17 pages
doi:10.1155/2010/697343
Research Article

On Invariant Tori of Nearly Integrable Hamiltonian Systems with Quasiperiodic Perturbation

Dongfeng Zhang1 and Rong Cheng2

1Department of Mathematics, Southeast University, Nanjing 210096, China
2College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, China

Received 2 September 2010; Accepted 25 October 2010

Academic Editor: Marlène Frigon

Copyright © 2010 Dongfeng Zhang and Rong Cheng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.