Uniform hyperbolicity revisited: index of periodic points and equidimensional cycles

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MetadadosDescriçãoIdioma
Autor(es): dc.creatorBessa, Mário-
Autor(es): dc.creatorRocha, Jorge-
Autor(es): dc.creatorVarandas, Paulo-
Data de aceite: dc.date.accessioned2025-08-21T15:23:22Z-
Data de disponibilização: dc.date.available2025-08-21T15:23:22Z-
Data de envio: dc.date.issued2023-05-25-
Data de envio: dc.date.issued2023-05-25-
Data de envio: dc.date.issued2018-
Fonte completa do material: dc.identifierhttp://hdl.handle.net/10400.2/13835-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/10400.2/13835-
Descrição: dc.descriptionIn this paper, we revisit uniformly hyperbolic basic sets and the domination of Oseledets splittings at periodic points. We prove that periodic points with simple Lyapunov spectrum are dense in non-trivial basic pieces of Cr-residual diffeomorphisms on three-dimensional manifolds (r>=1). In the case of the C1-topology, we can prove that either all periodic points of a hyperbolic basic piece for a diffeomorphism f have simple spectrum C1 -robustly (in which case f has a finest dominated splitting into one-dimensional sub-bundles and all Lyapunov exponent functions of f are continuous in the weak∗ -topology) or it can be C1-approximated by an equidimensional cycle associated to periodic points with robust different signatures. The latter can be used as a mechanism to guarantee the coexistence of infinitely many periodic points with different signatures.-
Descrição: dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico [grant number 301201/2016-1]; FCT (‘Fundação para a Ciência e a Tecnologia’) through the Centro de Matemática e Aplicações (CMA-UBI), Universidade da Beira Interior [project number UID/MAT/00212/2013]; CMUP [grant number UID/MAT/ 00144/2013]; FEDER [agreement number PT2020]; PTDC/MAT- CAL/3884/2014; BREUDS; CNPq-Brazil [grant number PQ E-Fomento 301201/2016-1].-
Descrição: dc.descriptioninfo:eu-repo/semantics/publishedVersion-
Formato: dc.formatapplication/pdf-
Idioma: dc.languageen-
Publicador: dc.publisherTaylor & Francis-
Relação: dc.relationCenter of Mathematics and Applications of University of Beira Interior-
Relação: dc.relationCentre for Mathematics of the University of Porto-
Palavras-chave: dc.subjectUniform hyperbolicity-
Palavras-chave: dc.subjectPeriodic points-
Palavras-chave: dc.subjectFinest dominated splitting-
Palavras-chave: dc.subjectOseledets splitting-
Palavras-chave: dc.subjectLyapunov exponents-
Título: dc.titleUniform hyperbolicity revisited: index of periodic points and equidimensional cycles-
Aparece nas coleções:Repositório Aberto - Universidade Aberta (Portugal)

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