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Publicação
Hamiltonian elliptic dynamics on symplectic $4$-manifolds
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Resumo(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.
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Contexto Educativo
Citação
M. Bessa, J. L. Dias, Hamiltonian elliptic dynamics on symplectic $4$-manifolds, Proceedings of the American Mathematical Society, 137, 2, 585-592, 2009
Editora
AMS - American Mathematical Society