Publication
Skew product cycles with rich dynamics: from totally non-hyperbolic dynamics to fully prevalent hyperbolicity
dc.contributor.author | Díaz, Lorenzo J. | |
dc.contributor.author | Esteves, Salete | |
dc.contributor.author | Rocha, Jorge | |
dc.date.accessioned | 2016-03-11T10:00:44Z | |
dc.date.available | 2016-03-11T10:00:44Z | |
dc.date.issued | 2016 | |
dc.description.abstract | We 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.sponsorship | This 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.citation | Díaz, 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. 1-40 | pt_PT |
dc.identifier.doi | 10.1080/14689367.2015.1085492 | pt_PT |
dc.identifier.issn | 1468-9367 | |
dc.identifier.uri | http://hdl.handle.net/10198/12789 | |
dc.language.iso | eng | pt_PT |
dc.peerreviewed | yes | pt_PT |
dc.publisher | Taylor & Francis | pt_PT |
dc.relation | SFRH/BD/49735/2009 | pt_PT |
dc.relation | Nonuniformly Hyperbolic Dynamics | |
dc.relation | CICLOS HETERODIMENSIONAIS MONÓTONOS | |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | pt_PT |
dc.subject | Bifurcation | pt_PT |
dc.subject | Heterodimensional cycle | pt_PT |
dc.subject | Homoclinic class | pt_PT |
dc.subject | Hyperbolicity | pt_PT |
dc.subject | Iterated function system | pt_PT |
dc.subject | Skew product | pt_PT |
dc.title | Skew product cycles with rich dynamics: from totally non-hyperbolic dynamics to fully prevalent hyperbolicity | pt_PT |
dc.type | journal article | |
dspace.entity.type | Publication | |
oaire.awardTitle | Nonuniformly Hyperbolic Dynamics | |
oaire.awardTitle | CICLOS HETERODIMENSIONAIS MONÓTONOS | |
oaire.awardURI | info:eu-repo/grantAgreement/FCT/5876-PPCDTI/PTDC%2FMAT%2F099493%2F2008/PT | |
oaire.awardURI | info:eu-repo/grantAgreement/FCT//SFRH%2FBD%2F27674%2F2006/PT | |
oaire.citation.conferencePlace | OXON, ENGLAND | pt_PT |
oaire.citation.endPage | 40 | pt_PT |
oaire.citation.issue | 1 | pt_PT |
oaire.citation.startPage | 1 | pt_PT |
oaire.citation.title | Dynamical Systems: An International Journal | pt_PT |
oaire.citation.volume | 31 | pt_PT |
oaire.fundingStream | 5876-PPCDTI | |
person.familyName | Esteves | |
person.givenName | Salete | |
person.identifier.ciencia-id | 411F-4C00-6212 | |
person.identifier.orcid | 0000-0002-1353-8462 | |
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 | |
rcaap.rights | restrictedAccess | pt_PT |
rcaap.type | article | pt_PT |
relation.isAuthorOfPublication | fda6f257-f565-4810-b563-6d5a6d0b7021 | |
relation.isAuthorOfPublication.latestForDiscovery | fda6f257-f565-4810-b563-6d5a6d0b7021 | |
relation.isProjectOfPublication | 113edfc0-16da-4ad2-b1c6-d38d1eb0acb3 | |
relation.isProjectOfPublication | be1bb8d2-0a33-41d4-84db-e640275b0260 | |
relation.isProjectOfPublication.latestForDiscovery | 113edfc0-16da-4ad2-b1c6-d38d1eb0acb3 |
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