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arXiv · 1107.4286

Creation of Homoclinic Tangencies in Hamiltonians by the Suspension of Poincar\'e Sections

Mário Bessa·João Lopes Dias
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Abstract

In this note we show that for any Hamiltonian defined on a symplectic 4-manifold M and any point p in M, there exists a C2-close Hamiltonian whose regular energy surface through p is either Anosov or it contains a homoclinic tangency. Our result is based on a general construction of Hamiltonian suspensions for given symplectomorphisms on Poincar\'e sections already known to yield similar properties.

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Mário Bessa, João Lopes Dias. 2011-07-21. Creation of Homoclinic Tangencies in Hamiltonians by the Suspension of Poincar\'e Sections. https://arxiv.org/abs/1107.4286

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