Persistence of Hyperbolic Tori in Generalized Hamiltonian Systems

Liu, Zhenxin; Yihe, Dalai; Huang, Qingdao

Persistence of Hyperbolic Tori in Generalized Hamiltonian Systems

Authors

Liu, Zhenxin

Yihe, Dalai

Huang, Qingdao

Description

In this paper we prove the persistence of hyperbolic invariant tori in generalized Hamiltonian systems, which may admit a distinct number of action and angle variables. The systems under consideration can be odd dimensional in tangent direction. Our results generalize the well-known results of Graff and Zehnder in standard Hamiltonians. In our case the unperturbed Hamiltonian systems may be degenerate. We also consider the persistence problem of hyperbolic tori on sub-manifolds.
LaTeX, 17 pages