Randomness in Deterministic Dynamical Systems and Applications

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Hamiltonian suspension of perturbed Poincaré sections and an application

Publication . Bessa, Mário; Dias, João Lopes

We construct a Hamiltonian suspension for a given symplectomorphism which is the per- turbation 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 C2-close Hamiltonian whose regular energy surface through p is either Anosov or contains a homo- clinic tangency.

2014Journal article

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