Expansiveness and hyperbolicity in convex billiards

Detalhes bibliográficos
Autor(a) principal: Bessa, Mário
Data de Publicação: 2021
Outros Autores: Dias, João 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/10400.2/13899
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 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.
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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 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.SpringerRepositório AbertoBessa, MárioDias, João LopesTorres, Maria Joana2023-05-30T10:40:55Z20212021-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/13899engBessa, M., Dias, J.L. & Torres, M.J. Expansiveness and Hyperbolicity in Convex Billiards. Regul. Chaot. Dyn. 26, 756–762 (2021)10.1134/S1560354721060125info: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:RCAAP2023-11-16T15:46:14Zoai:repositorioaberto.uab.pt:10400.2/13899Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:52:48.339366Repositório 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, João Lopes
Torres, Maria Joana
author_role author
author2 Dias, João Lopes
Torres, Maria Joana
author2_role author
author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Bessa, Mário
Dias, João 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 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.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-01-01T00:00:00Z
2023-05-30T10:40:55Z
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/10400.2/13899
url http://hdl.handle.net/10400.2/13899
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Bessa, M., Dias, J.L. & Torres, M.J. Expansiveness and Hyperbolicity in Convex Billiards. Regul. Chaot. Dyn. 26, 756–762 (2021)
10.1134/S1560354721060125
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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