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Uniform hyperbolicity revisited: index of periodic points and equidimensional cycles

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dc.contributor.authorBessa, Mario
dc.contributor.authorRocha, Jorge
dc.contributor.authorVarandas, Paulo
dc.date.accessioned2020-02-05T10:11:13Z
dc.date.available2020-02-05T10:11:13Z
dc.date.issued2018
dc.description.abstractIn this paper, we revisit uniformly hyperbolic basic sets and the dom- ination of Oseledets splittings at periodic points. We prove that peri- odic 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 diffeomor- phism f have simple spectrum C1 -robustly (in which case f has a finest dominated splitting into one-dimensional sub-bundles and all Lya- punov 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.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.doi10.1080/14689367.2018.1433818pt_PT
dc.identifier.urihttp://hdl.handle.net/10400.6/9020
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.subjectUniform hyperbolicitypt_PT
dc.subjectPeriodic pointspt_PT
dc.subjectFinest dominated splittingpt_PT
dc.subjectOseledets splittingpt_PT
dc.subjectLyapunov exponentspt_PT
dc.titleUniform hyperbolicity revisited: index of periodic points and equidimensional cyclespt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/5876/UID%2FMAT%2F00212%2F2013/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/5876/UID%2FMAT%2F00144%2F2013/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/3599-PPCDT/PTDC%2FMAT-CAL%2F3884%2F2014/PT
oaire.citation.issue4pt_PT
oaire.citation.titleDynamical Systems An international Journalpt_PT
oaire.citation.volume33pt_PT
oaire.fundingStream5876
oaire.fundingStream5876
oaire.fundingStream3599-PPCDT
person.familyNameBessa
person.familyNameVarandas
person.givenNameMário
person.givenNamePaulo
person.identifierhttps://scholar.google.com/citations?user=088yCR4AAAAJ&hl=pt-PT
person.identifierR-002-RFA
person.identifier.ciencia-idC21A-EEC0-A3EF
person.identifier.ciencia-id0C1A-DC54-F959
person.identifier.orcid0000-0002-1758-2225
person.identifier.orcid0000-0002-0902-8718
person.identifier.ridI-7729-2013
person.identifier.scopus-author-id25626996500
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.embargofctCopyright cedido à editora no momento da publicaçãopt_PT
rcaap.rightsclosedAccesspt_PT
rcaap.typearticlept_PT
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