Bessa, MárioDias, João Lopes2023-05-262023-05-262014M. Bessa, J. L. Dias, Hamiltonian suspension of perturbed Poincaré sections and an application, 157, 1, 101-112, 2014http://hdl.handle.net/10400.2/13861We 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.engjournal article10.1017/S0305004114000140