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

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
JournalNonlinearity
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.
TypeArticle
URIhttps://hdl.handle.net/1822/25416
DOI10.1088/0951-7715/26/10/2851
ISSN0951-7715
Publisher versionhttp://stacks.iop.org/0951-7715/26/2851
Peer-Reviewedyes
AccessRestricted access (UMinho)
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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