Bessa, MárioDias, João Lopes2023-10-132023-10-132009Bessa, Mário and João Lopes Dias .(2009). “Hamiltonian elliptic dynamics on symplectic 4-manifolds” . Proceedings American Mathematical Society, Volume 137, Number 2: pp. 585–592 (Search PDF in 2023).http://hdl.handle.net/10400.5/28970We 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.engHamiltonian FunctionsElliptic DynamicsGeometric and Probabilistic Perspectivejournal article1088-6826