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TitleShades of hyperbolicity for Hamiltonians
Author(s)Bessa, Mário
Rocha, Jorge
Torres, M. J.
KeywordsHamiltonian vector field
Structural stability
Dominated splitting
Elliptic closed orbits
Issue date2013
PublisherIOP Publishing
Abstract(s)We prove that a Hamiltonian system H \in C^2(M,R) is globally hyperbolic if any of the following statements holds: H is robustly topologically stable; H is stably shadowable; H is stably expansive; and H has the stable weak specification property. Moreover, we prove that, for a C^2-generic Hamiltonian H, the union of the partially hyperbolic regular energy hypersurfaces and the closed elliptic orbits, forms a dense subset of M. As a consequence, any robustly transitive regular energy hypersurface of a C^2-Hamiltonian is partially hyperbolic. Finally, we prove that stably weakly shadowable regular energy hypersurfaces are partially hyperbolic.
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AccessRestricted access (UMinho)
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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