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Hamiltonian suspension of perturbed Poincaré sections and an application

Published online by Cambridge University Press:  09 April 2014

MÁRIO BESSA  and
JOÁO LOPES DIAS
MÁRIO BESSA
Affiliation:
Universidade da Beira Interior, Rua Marquês d'Ávila e Bolama, 6201-001 Covilhã, Portugal. e-mail: bessa@ubi.pt
JOÁO LOPES DIAS
Affiliation:
Universidade Técnica de Lisboa- ISEG, Rua do Quelhas 6, 1200-781 Lisboa, Portugal. e-mail: jldias@iseg.utl.pt
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Abstract

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 C2-close Hamiltonian whose regular energy surface through p is either Anosov or contains a homoclinic tangency.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 157 , Issue 1 , July 2014 , pp. 101 - 112
Copyright
Copyright © Cambridge Philosophical Society 2014 

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