Expansiveness and hyperbolicity in convex billiards

Detalhes bibliográficos
Autor(a) principal: Bessa, Mário
Data de Publicação: 2021
Outros Autores: Dias, José Lopes, Torres, Maria Joana
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.5/28886
Resumo: We 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 fB is expansive on the maximal invariant set ΛB,U = .Ո n∈Z f n 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 fB in ΛB,U is uniformly hyperbolic. In addition, we show that this property also holds for a generic choice among billiards which are expansive
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spelling Expansiveness and hyperbolicity in convex billiardsConvex Planar BilliardsHyperbolic SetsExpansivenessWe 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 fB is expansive on the maximal invariant set ΛB,U = .Ո n∈Z f n 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 fB in ΛB,U is uniformly hyperbolic. In addition, we show that this property also holds for a generic choice among billiards which are expansiveSpringer NatureRepositório da Universidade de LisboaBessa, MárioDias, José LopesTorres, Maria Joana2023-10-04T09:52:24Z20212021-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/28886engBessa, Mário; José Lopes Dias and Maria Joana Torres .(2021). “Expansiveness and hyperbolicity in convex billiards”. Regular and Chaotic Dynamics, Vol 26, No. 6: pp. 756-762. (Search PDF in 2023)DOI: 10.1134/S15603547210601251468 - 4845info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-10-22T01:31:58Zoai:www.repository.utl.pt:10400.5/28886Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:33:56.415915Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Expansiveness and hyperbolicity in convex billiards
title Expansiveness and hyperbolicity in convex billiards
spellingShingle Expansiveness and hyperbolicity in convex billiards
Bessa, Mário
Convex Planar Billiards
Hyperbolic Sets
Expansiveness
title_short Expansiveness and hyperbolicity in convex billiards
title_full Expansiveness and hyperbolicity in convex billiards
title_fullStr Expansiveness and hyperbolicity in convex billiards
title_full_unstemmed Expansiveness and hyperbolicity in convex billiards
title_sort Expansiveness and hyperbolicity in convex billiards
author Bessa, Mário
author_facet Bessa, Mário
Dias, José Lopes
Torres, Maria Joana
author_role author
author2 Dias, José Lopes
Torres, Maria Joana
author2_role author
author
dc.contributor.none.fl_str_mv Repositório da Universidade de Lisboa
dc.contributor.author.fl_str_mv Bessa, Mário
Dias, José Lopes
Torres, Maria Joana
dc.subject.por.fl_str_mv Convex Planar Billiards
Hyperbolic Sets
Expansiveness
topic Convex Planar Billiards
Hyperbolic Sets
Expansiveness
description We 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 fB is expansive on the maximal invariant set ΛB,U = .Ո n∈Z f n 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 fB in ΛB,U is uniformly hyperbolic. In addition, we show that this property also holds for a generic choice among billiards which are expansive
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-01-01T00:00:00Z
2023-10-04T09:52:24Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.5/28886
url http://hdl.handle.net/10400.5/28886
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Bessa, Mário; José Lopes Dias and Maria Joana Torres .(2021). “Expansiveness and hyperbolicity in convex billiards”. Regular and Chaotic Dynamics, Vol 26, No. 6: pp. 756-762. (Search PDF in 2023)
DOI: 10.1134/S1560354721060125
1468 - 4845
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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dc.publisher.none.fl_str_mv Springer Nature
publisher.none.fl_str_mv Springer Nature
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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