Publication
Uniform hyperbolicity revisited: index of periodic points and equidimensional cycles
| dc.contributor.author | Bessa, Mário | |
| dc.contributor.author | Rocha, Jorge | |
| dc.contributor.author | Varandas, Paulo | |
| dc.date.accessioned | 2023-05-25T09:54:22Z | |
| dc.date.available | 2023-05-25T09:54:22Z | |
| dc.date.issued | 2018 | |
| dc.description.abstract | In 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. | pt_PT |
| dc.description.sponsorship | Conselho 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]. | pt_PT |
| dc.description.version | info:eu-repo/semantics/publishedVersion | pt_PT |
| dc.identifier.citation | M. Bessa, J. Rocha, P. Varandas, Uniform hyperbolicity revisited: index of periodic points and equidimensional cycles, Dynamical Systems, 33, 4, 691-707, 2018 | pt_PT |
| dc.identifier.doi | 10.1080/14689367.2018.1433818 | pt_PT |
| dc.identifier.uri | http://hdl.handle.net/10400.2/13835 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.publisher | Taylor & Francis | pt_PT |
| dc.relation | Center of Mathematics and Applications of University of Beira Interior | |
| dc.relation | Centre for Mathematics of the University of Porto | |
| dc.subject | Uniform hyperbolicity | pt_PT |
| dc.subject | Periodic points | pt_PT |
| dc.subject | Finest dominated splitting | pt_PT |
| dc.subject | Oseledets splitting | pt_PT |
| dc.subject | Lyapunov exponents | pt_PT |
| dc.title | Uniform hyperbolicity revisited: index of periodic points and equidimensional cycles | pt_PT |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.awardTitle | Center of Mathematics and Applications of University of Beira Interior | |
| oaire.awardTitle | Centre for Mathematics of the University of Porto | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UID%2FMAT%2F00212%2F2013/PT | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UID%2FMAT%2F00144%2F2013/PT | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/3599-PPCDT/PTDC%2FMAT-CAL%2F3884%2F2014/PT | |
| oaire.citation.endPage | 707 | pt_PT |
| oaire.citation.issue | 4 | pt_PT |
| oaire.citation.startPage | 691 | pt_PT |
| oaire.citation.title | Dynamical Systems | pt_PT |
| oaire.citation.volume | 33 | pt_PT |
| oaire.fundingStream | 6817 - DCRRNI ID | |
| oaire.fundingStream | 6817 - DCRRNI ID | |
| oaire.fundingStream | 3599-PPCDT | |
| person.familyName | Bessa | |
| person.familyName | Rodrigues Pinto Varandas | |
| person.givenName | Mário | |
| person.givenName | Paulo César | |
| person.identifier | https://scholar.google.com/citations?user=088yCR4AAAAJ&hl=pt-PT | |
| person.identifier.ciencia-id | C21A-EEC0-A3EF | |
| person.identifier.ciencia-id | 0C1A-DC54-F959 | |
| person.identifier.orcid | 0000-0002-1758-2225 | |
| person.identifier.orcid | 0000-0002-0902-8718 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| rcaap.rights | restrictedAccess | pt_PT |
| rcaap.type | article | pt_PT |
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