08-16 Mario Bessa and Joao Lopes Dias

Hamiltonian elliptic dynamics on symplectic 4-manifolds (266K, pdf) Jan 21, 08

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Abstract. We consider C^2 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 C^2-generic Hamiltonian the elliptic closed orbits are generic.

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