Please use this identifier to cite or link to this item: https://hdl.handle.net/1822/25416

 Title: Shades of hyperbolicity for Hamiltonians Author(s): Bessa, MárioRocha, JorgeTorres, M. J. Keywords: Hamiltonian vector fieldStructural stabilityDominated splittingElliptic closed orbits Issue date: 2013 Publisher: IOP Publishing Journal: Nonlinearity 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. Type: Article URI: https://hdl.handle.net/1822/25416 DOI: 10.1088/0951-7715/26/10/2851 ISSN: 0951-7715 Publisher version: http://stacks.iop.org/0951-7715/26/2851 Peer-Reviewed: yes Access: Restricted access (UMinho) Appears in Collections: CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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