Hamiltonian Suspension of Perturbed Poincaré Sections and an Application
نویسنده
چکیده
We construct a Hamiltonian suspension for a given symplectomorphism which is the perturbation of a Poincaré map. This is especially useful for the conversion of perturbative results between symplectomorphisms and Hamiltonian flows in any dimension 2d. As an application, using known properties of area-preserving maps, we prove that for any Hamiltonian defined on a symplectic 4-manifold M and any point p ∈ M , there exists a C-close Hamiltonian whose regular energy surface through p is either Anosov or contains a homoclinic tangency. MSC 2000: Primary: 37J45, 37D05 ; Secondary: 37D20. keywords: Hamiltonian vector field, Anosov flow, elliptic point, homoclinic tangency.
منابع مشابه
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تاریخ انتشار 2012