Bessa, MárioLopes Dias, João2023-05-312023-05-312009M. Bessa, J. L. Dias, Hamiltonian elliptic dynamics on symplectic $4$-manifolds, Proceedings of the American Mathematical Society, 137, 2, 585-592, 2009http://hdl.handle.net/10400.2/13931We consider C2-Hamiltonian functions on compact 4-dimensional symplectic manifolds to study the 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.engjournal article10.1090/S0002-9939-08-09578-6