Persistence of lower dimensional invariant tori on sub-manifolds in Hamiltonian systems

Zhenxin Liu

Persistence of lower dimensional invariant tori on sub-manifolds in Hamiltonian systems

Dynamical Systems 2007-05-23 v1

Authors: Zhenxin Liu

Abstract

Chow, Li and Yi in [2] proved that the majority of the unperturbed tori {\it on sub-manifolds} will persist for standard Hamiltonian systems. Motivated by their work, in this paper, we study the persistence and tangent frequencies preservation of lower dimensional invariant tori on smooth sub-manifolds for real analytic, nearly integrable Hamiltonian systems. The surviving tori might be elliptic, hyperbolic, or of mixed type.

Keywords

Hamiltonian systems invariant tori sub-manifolds persistence tangent frequencies

Cite

@article{arxiv.math/0503530,
  title  = {Persistence of lower dimensional invariant tori on sub-manifolds in Hamiltonian systems},
  author = {Zhenxin Liu},
  journal= {arXiv preprint arXiv:math/0503530},
  year   = {2007}
}

Comments

25 pages. To appear in Nonlinear Analysis: TMA

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