Persistence of hyperbolic tori in Hamiltonian systems |
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Authors: | Yong Li Yingfei Yi |
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Institution: | a Department of Mathematics, Jilin University, Changchun 130012, PR China b School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA |
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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. |
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Keywords: | 37J40 |
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