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

Chow et al. (J. Non. Sci. 12 (2002) 585) proved that the majority of the unperturbed tori 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 smoot...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinear analysis 2005-06, Vol.61 (8), p.1319-1342
Main Author: Liu, Zhenxin
Format: Article
Language:English
Subjects:
Exact sciences and technology
Global analysis, analysis on manifolds
Hamiltonian system
KAM theorem
Lower dimensional invariant tori
Mathematics
Persistence on sub-manifolds
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Chow et al. (J. Non. Sci. 12 (2002) 585) proved that the majority of the unperturbed tori 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.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2005.01.106