- 08-16 Mario Bessa and Joao Lopes Dias
- Hamiltonian elliptic dynamics on symplectic 4-manifolds
Jan 21, 08
(auto. generated pdf),
of related papers
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.