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Expansiveness and hyperbolicity in convex billiards

2021Journal article Open access
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dc.contributor.authorBessa, Mário
dc.contributor.authorDias, João Lopes
dc.contributor.authorTorres, Maria Joana
dc.date.accessioned2023-05-30T10:40:55Z
dc.date.available2023-05-30T10:40:55Z
dc.date.issued2021
dc.description.abstractWe say that a convex planar billiard table B is C2-stably expansive on a fixed open subset U of the phase space if its billiard map f_B is expansive on the maximal invariant set Λ_{B,U}, and this property holds under C2-perturbations of the billiard table. In this note we prove for such billiards that the closure of the set of periodic points of f_B in Λ_{B,U} is uniformly hyperbolic. In addition, we show that this property also holds for a generic choice among billiards which are expansive.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationBessa, M., Dias, J.L. & Torres, M.J. Expansiveness and Hyperbolicity in Convex Billiards. Regul. Chaot. Dyn. 26, 756–762 (2021)pt_PT
dc.identifier.doi10.1134/S1560354721060125pt_PT
dc.identifier.urihttp://hdl.handle.net/10400.2/13899
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherSpringerpt_PT
dc.relationCenter of Mathematics of the University of Minho
dc.relationCenter of Mathematics of the University of Minho
dc.relation.publisherversionhttps://link.springer.com/article/10.1134/S1560354721060125pt_PT
dc.subjectConvex planar billiardspt_PT
dc.subjectHyperbolic setspt_PT
dc.subjectExpansivenesspt_PT
dc.titleExpansiveness and hyperbolicity in convex billiardspt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleCenter of Mathematics of the University of Minho
oaire.awardTitleCenter of Mathematics of the University of Minho
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/3599-PPCDT/PTDC%2FMAT-PUR%2F29126%2F2017/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00013%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F00013%2F2020/PT
oaire.citation.endPage762pt_PT
oaire.citation.issue6pt_PT
oaire.citation.startPage756pt_PT
oaire.citation.titleRegular and Chaotic Dynamicspt_PT
oaire.citation.volume26pt_PT
oaire.fundingStream3599-PPCDT
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream6817 - DCRRNI ID
person.familyNameBessa
person.familyNameDias
person.familyNameTorres
person.givenNameMário
person.givenNameJoão Lopes
person.givenNameMaria Joana
person.identifierhttps://scholar.google.com/citations?user=088yCR4AAAAJ&hl=pt-PT
person.identifier.ciencia-idC21A-EEC0-A3EF
person.identifier.ciencia-idA01A-369C-B7B3
person.identifier.ciencia-id4612-CB41-300A
person.identifier.orcid0000-0002-1758-2225
person.identifier.orcid0000-0002-2089-7308
person.identifier.orcid0000-0002-3673-5776
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.rightsopenAccesspt_PT
rcaap.typearticlept_PT
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