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- W1545710635 abstract "AbstractIn this paper we prove the persistence of hyperbolic invariant tori in generalized Hamil-tonian systems, which may admit a distinct number of action and angle variables. Thesystems under consideration can be odd dimensional in tangent direction. Our results gen-eralize the well-known results of Graff and Zehnder in standard Hamiltonians. In our casethe unperturbed Hamiltonian systems may be degenerate. We also consider the persistenceproblem of hyperbolic tori on sub-manifolds. Keywords : hyperbolic invariant tori; KAM theorem; generalized Hamiltonian systems 1 Introduction and Main Result According to the celebrated KAM (Kolmogorov-Arnold-Moser) theory, we know that mostof invariant tori of integrable Hamiltonians persist under a small perturbation. In theircase, the Hamiltonian is standard and the dimension of invariant tori equals the degree offreedom, i.e., the “highest dimensional tori”. However, some Hamiltonian systems’ highestdimensional tori cannot survive the perturbations, but some tori which have lower dimensioncan be persisted under small perturbations, which are called lower dimensional invariant tori.In 1965, Melnikov" @default.
- W1545710635 created "2016-06-24" @default.
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- W1545710635 date "2005-01-01" @default.
- W1545710635 modified "2023-09-27" @default.
- W1545710635 title "Persistence of Hyperbolic Tori in Generalized Hamiltonian Systems" @default.
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