Persistence of Hyperbolic Tori in Generalized Hamiltonian Systems

Zhenxin Liu, Dalai Yihe, Qingdao Huang

Published 2006-10-21Version 1

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.