Persistence of Hyperbolic Tori in Generalized Hamiltonian Systems

Details Persistence of Hyperbolic Tori in Generalized Hamiltonian Systems Persistence of Hyperbolic Tori in Generalized Hamiltonian Systems

2006-10-21

arxiv.org/abs/math/0610641v1

Northeast. Math. J. 21 (4) (2005), 447-464

Mathematics

Dynamical Systems

LaTeX, 17 pages

Scientific paper

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.

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