Hamiltonian elliptic dynamics on symplectic $4$-manifolds

Bessa, Mário; Lopes Dias, João

http://hdl.handle.net/10400.2/13931

Use this identifier to reference this record.

Name:	Description:	Size:	Format:
PAMS.pdf		171.66 KB	Adobe PDF	Download

Send Feedback

Authors

Bessa, Mário

Lopes Dias, João

Abstract(s)

We 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.

URI

http://hdl.handle.net/10400.2/13931

Citation

M. Bessa, J. L. Dias, Hamiltonian elliptic dynamics on symplectic $4$-manifolds, Proceedings of the American Mathematical Society, 137, 2, 585-592, 2009