Title:
Persistence of Hyperbolic Tori in Hamiltonian Systems
Persistence of Hyperbolic Tori in Hamiltonian Systems
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Author(s)
Li, Yong
Yi, Yingfei
Yi, Yingfei
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Abstract
We generalize the well-known result of Graff and Zehnder on the persistence of hyperbolic invariant tori in Hamiltonian systems by considering non-Floquet, frequency varying normal forms and allowing the degeneracy of
the unperturbed frequencies. The preservation of part or full frequency components associated to the degree of non-degeneracy is considered. As applications, we consider the persistence problem of hyperbolic tori on a submanifold
of a nearly integrable Hamiltonian system and the persistence problem of a fixed invariant hyperbolic torus in a non-integrable Hamiltonian system.
Sponsor
The first author is partially supported by NSFC 19971042, National 973 Key Project of China: Nonlinearity, the outstanding young's project of Ministry of Education of China, and National outstanding young's award of China. The second author was partially supported by NSF grant DMS0204119.
Date Issued
1999
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Pre-print