Hamiltonian elliptic dynamics on symplectic 4-manifolds

Mario Bessa; Joao Lopes Dias

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arXiv · 0801.3072

Hamiltonian elliptic dynamics on symplectic 4-manifolds

Mario Bessa·Joao Lopes Dias

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Abstract

We consider C2 Hamiltonian functions on compact 4-dimensional symplectic manifolds to study elliptic dynamics of the Hamiltonian flow, namely the so-called Newhouse dichotomy. We show that for any open set U intersecting a far from Anosov regular energy surface, there is a nearby Hamiltonian having an elliptic closed orbit through U. Moreover, this implies that for far from Anosov regular energy surfaces of a C2-generic Hamiltonian the elliptic closed orbits are generic.

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Mario Bessa, Joao Lopes Dias. 2008-01-21. Hamiltonian elliptic dynamics on symplectic 4-manifolds. https://arxiv.org/abs/0801.3072

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