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Hamiltonian elliptic dynamics on symplectic  -manifolds
Author(s):
Mário
Bessa;
João
Lopes
Dias
Journal:
Proc. Amer. Math. Soc.
137
(2009),
585-592.
MSC (2000):
Primary 37J25, 37D30;
Secondary 37C27
Posted:
August 20, 2008
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Abstract:
We consider  -Hamiltonian functions on compact  -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  intersecting a far from Anosov regular energy surface, there is a nearby Hamiltonian having an elliptic closed orbit through  . Moreover, this implies that, for far from Anosov regular energy surfaces of a  -generic Hamiltonian, the elliptic closed orbits are generic.
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Additional Information:
Mário
Bessa
Affiliation:
Centro de Matemática da Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal
Email:
bessa@fc.up.pt
João
Lopes
Dias
Affiliation:
Departamento de Matemática, ISEG, Universidade Técnica de Lisboa, Rua do Quelhas 6, 1200-781 Lisboa, Portugal
Email:
jldias@iseg.utl.pt
DOI:
10.1090/S0002-9939-08-09578-6
PII:
S 0002-9939(08)09578-6
Received by editor(s):
January 23, 2008
Posted:
August 20, 2008
Communicated by:
Bryna Kra
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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