Hamiltonian suspension of perturbed Poincaré sections and an application

Bessa, Mário; Dias, João Lopes

http://hdl.handle.net/10400.2/13861

Use this identifier to reference this record.

Name:	Description:	Size:	Format:
MPCPS2.pdf		261.06 KB	Adobe PDF	Download

Send Feedback

Authors

Bessa, Mário

Dias, João Lopes

Abstract(s)

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.