Publicação
Expansiveness and hyperbolicity in convex billiards
| 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 |
|---|---|
| Autores principais: | Bessa, Mário |
| Outros Autores: | Dias, José Lopes; Torres, Maria Joana |
| Assunto: | Convex Planar Billiards Hyperbolic Sets Expansiveness |
| Ano: | 2021 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório da Universidade de Lisboa |
| _version_ | 1866810873883918336 |
|---|---|
| author | Bessa, Mário |
| author2 | Dias, José Lopes Torres, Maria Joana |
| author2_role | author author |
| author_facet | Bessa, Mário Dias, José Lopes Torres, Maria Joana |
| author_role | author |
| contributor_name_str_mv | Repositório Científico de Acesso Aberto da ULisboa |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Bessa, Mário\"},{\"Person.name\":\"Dias, José Lopes\"},{\"Person.name\":\"Torres, Maria Joana\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | Repositório Científico de Acesso Aberto da ULisboa |
| datacite.creators.creator.creatorName.fl_str_mv | Bessa, Mário Dias, José Lopes Torres, Maria Joana |
| datacite.date.Accepted.fl_str_mv | 2021-01-01T00:00:00Z |
| datacite.date.available.fl_str_mv | 2023-10-04T09:52:24Z |
| datacite.date.embargoed.fl_str_mv | 2023-10-04T09:52:24Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Convex Planar Billiards Hyperbolic Sets Expansiveness |
| datacite.titles.title.fl_str_mv | Expansiveness and hyperbolicity in convex billiards |
| dc.contributor.none.fl_str_mv | Repositório Científico de Acesso Aberto da ULisboa |
| dc.creator.none.fl_str_mv | Bessa, Mário Dias, José Lopes Torres, Maria Joana |
| dc.date.Accepted.fl_str_mv | 2021-01-01T00:00:00Z |
| dc.date.available.fl_str_mv | 2023-10-04T09:52:24Z |
| dc.date.embargoed.fl_str_mv | 2023-10-04T09:52:24Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10400.5/28886 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Springer Nature |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Convex Planar Billiards Hyperbolic Sets Expansiveness |
| dc.title.fl_str_mv | Expansiveness and hyperbolicity in convex billiards |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| 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 |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | article |
| fulltext.url.fl_str_mv | https://repositorio.ulisboa.pt/bitstreams/403c6c7f-3d08-487a-9187-6b7c4992bc7e/download |
| id | ul_991a19c09f8dcd7ba7929fa2f4e0ea0b |
| identifier.url.fl_str_mv | http://hdl.handle.net/10400.5/28886 |
| instacron_str | ul |
| institution | Universidade de Lisboa |
| instname_str | Universidade de Lisboa |
| language | eng |
| network_acronym_str | ul |
| network_name_str | Repositório da Universidade de Lisboa |
| oai_identifier_str | oai:repositorio.ulisboa.pt:10400.5/28886 |
| organization_str_mv | urn:organizationAcronym:ul |
| person_str_mv | Bessa, Mário Dias, José Lopes Torres, Maria Joana |
| publishDate | 2021 |
| publisher.none.fl_str_mv | Springer Nature |
| reponame_str | Repositório da Universidade de Lisboa |
| repository_id_str | urn:repositoryAcronym:ul |
| service_str_mv | urn:repositoryAcronym:ul |
| spelling | engSpringer Naturept_PTWe 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 expansiveapplication/pdfpt_PTExpansiveness and hyperbolicity in convex billiardsBessa, MárioDias, José LopesTorres, Maria JoanaHostingInstitutionOrganizationalRepositório Científico de Acesso Aberto da ULisboae-mailmailto:repositorio@reitoria.ulisboa.ptrepositorio@reitoria.ulisboa.ptDOIIsPartOfDOI: 10.1134/S15603547210601252023-10-04T09:52:24Z20212021-01-01T00:00:00ZHandlehttp://hdl.handle.net/10400.5/28886http://purl.org/coar/access_right/c_abf2open accessConvex Planar BilliardsHyperbolic SetsExpansiveness513325 bytesliteraturehttp://purl.org/coar/resource_type/c_6501journal articlehttp://purl.org/coar/access_right/c_abf2application/pdffulltexthttps://repositorio.ulisboa.pt/bitstreams/403c6c7f-3d08-487a-9187-6b7c4992bc7e/download |
| spellingShingle | Expansiveness and hyperbolicity in convex billiards Bessa, Mário Convex Planar Billiards Hyperbolic Sets Expansiveness |
| status | SINGLETON |
| subject.fl_str_mv | Convex Planar Billiards Hyperbolic Sets Expansiveness |
| title | 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_short | Expansiveness and hyperbolicity in convex billiards |
| title_sort | Expansiveness and hyperbolicity in convex billiards |
| topic | Convex Planar Billiards Hyperbolic Sets Expansiveness |
| topic_facet | Convex Planar Billiards Hyperbolic Sets Expansiveness |
| url | http://hdl.handle.net/10400.5/28886 |
| visible | 1 |