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Hamiltonian elliptic dynamics on symplectic 4-manifolds

Authors
  • Bessa, Mario
  • Dias, Joao Lopes
Type
Published Article
Publication Date
Jan 21, 2008
Submission Date
Jan 21, 2008
Source
arXiv
License
Unknown
External links

Abstract

We consider C2 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 C2-generic Hamiltonian the elliptic closed orbits are generic.

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