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

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

2005-03-24

arxiv.org/abs/math/0503530v1

Mathematics

Dynamical Systems

25 pages. To appear in Nonlinear Analysis: TMA

Scientific paper

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.

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