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Skew product cycles with rich dynamics: from totally non-hyperbolic dynamics to fully prevalent hyperbolicity

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dc.contributor.authorDíaz, Lorenzo J.
dc.contributor.authorEsteves, Salete
dc.contributor.authorRocha, Jorge
dc.date.accessioned2016-03-11T10:00:44Z
dc.date.available2016-03-11T10:00:44Z
dc.date.issued2016
dc.description.abstractWe introduce a two-parameter family of partially hyperbolic' skew products (G(a, t)) maps with one dimensional centre direction. In this family, the parameter a models the central dynamics and the parameter t the unfolding of cycles (that occurs for t = 0). The parameter a also measures the central distortion' of the systems: for small a, the distortion of the systems is small and it increases and goes to infinity as a . The family (G(a, t)) displays some of the main characteristic properties of the unfolding of heterodimensional cycles as intermingled homoclinic classes of different indices and secondary bifurcations via collision of hyperbolic homoclinic classes. For a in (0, log2), the dynamics of (G(a, t)) is always non-hyperbolic after the unfolding of the cycle. However, for a > log4 intervals of t-parameters corresponding to hyperbolic dynamics appear and turn into totally prevalent as a (the density of hyperbolic parameters' goes to 1 as a ). The dynamics of the maps G(a, t) is described using a family of iterated function systems modelling the dynamics in the one-dimensional central direction.pt_PT
dc.description.sponsorshipThis paper is part of doctoral thesis of Salete Esteves partially supported by the project PEst-C/MAT/UI0144/2011 of FCT (Fundação para a Ciência e a Tecnologia, Portugal). Salete Esteves and Jorge Rocha were partially supported by the PTDC/MAT/099493/2008, SFRH/BD/27674/2006, and SFRH/BD/49735/2009. Lorenzo J. Díaz was partially supported by CNPq, Faperj, and Pronex (Brazil), Palis-Balzan project, and BREUDS. We thank the comments made by an anonymous referee.
dc.identifier.citationDíaz, Lorenzo J.; Esteves, Salete; Rocha, Jorge (2016). Skew product cycles with rich dynamics: from totally non-hyperbolic dynamics to fully prevalent hyperbolicity. Dynamical Systems. ISSN 1468-9367. 31:1, p. 1-40pt_PT
dc.identifier.doi10.1080/14689367.2015.1085492pt_PT
dc.identifier.issn1468-9367
dc.identifier.urihttp://hdl.handle.net/10198/12789
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherTaylor & Francispt_PT
dc.relationSFRH/BD/49735/2009pt_PT
dc.relationNonuniformly Hyperbolic Dynamics
dc.relationCICLOS HETERODIMENSIONAIS MONÓTONOS
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/pt_PT
dc.subjectBifurcationpt_PT
dc.subjectHeterodimensional cyclept_PT
dc.subjectHomoclinic classpt_PT
dc.subjectHyperbolicitypt_PT
dc.subjectIterated function systempt_PT
dc.subjectSkew productpt_PT
dc.titleSkew product cycles with rich dynamics: from totally non-hyperbolic dynamics to fully prevalent hyperbolicitypt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleNonuniformly Hyperbolic Dynamics
oaire.awardTitleCICLOS HETERODIMENSIONAIS MONÓTONOS
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/5876-PPCDTI/PTDC%2FMAT%2F099493%2F2008/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT//SFRH%2FBD%2F27674%2F2006/PT
oaire.citation.conferencePlaceOXON, ENGLANDpt_PT
oaire.citation.endPage40pt_PT
oaire.citation.issue1pt_PT
oaire.citation.startPage1pt_PT
oaire.citation.titleDynamical Systems: An International Journalpt_PT
oaire.citation.volume31pt_PT
oaire.fundingStream5876-PPCDTI
person.familyNameEsteves
person.givenNameSalete
person.identifier.ciencia-id411F-4C00-6212
person.identifier.orcid0000-0002-1353-8462
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
rcaap.rightsrestrictedAccesspt_PT
rcaap.typearticlept_PT
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