Ergodic properties of polygonal billiards with strongly contracting reflection laws

Detalhes bibliográficos
Autor(a) principal: Magno, Gianluigi Del
Data de Publicação: 2015
Outros Autores: Dias, João Lopes, Duarte, Pedro, Gaivão, José Pedro
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.5/9286
Resumo: We consider convex polygonal billiards with a reflection law that contracts the reflection angle towards the normal. Polygonal billiards with orthogonal reflections are called slap maps. For polygons without parallel sides facing each other, the slap map has a finite number of ergodic absolutely continuous invariant probability measures. We show that any billiard with a strongly contracting reflection law has the same number of ergodic SRB measures with the same mixing periods as the ergodic absolutely continuous invariant probabilities of its corresponding slap map. The case of billiards in regular polygons and triangles is studied in detail.
id RCAP_315a14bec043f37d59e83e25e6b03f44
oai_identifier_str oai:www.repository.utl.pt:10400.5/9286
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling Ergodic properties of polygonal billiards with strongly contracting reflection lawsWe consider convex polygonal billiards with a reflection law that contracts the reflection angle towards the normal. Polygonal billiards with orthogonal reflections are called slap maps. For polygons without parallel sides facing each other, the slap map has a finite number of ergodic absolutely continuous invariant probability measures. We show that any billiard with a strongly contracting reflection law has the same number of ergodic SRB measures with the same mixing periods as the ergodic absolutely continuous invariant probabilities of its corresponding slap map. The case of billiards in regular polygons and triangles is studied in detail.ISEG - CEMAPRERepositório da Universidade de LisboaMagno, Gianluigi DelDias, João LopesDuarte, PedroGaivão, José Pedro2015-10-02T14:00:12Z20152015-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/9286engMagno, Gianluigi Del ... [et al.] (2015). "Ergodic properties of polygonal billiards with strongly contracting reflection laws". Instituto Superior de Economia e Gestão – CEMAPRE preprintinfo: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:RCAAP2023-03-06T14:39:50Zoai:www.repository.utl.pt:10400.5/9286Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T16:56:06.759870Repositório 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 Ergodic properties of polygonal billiards with strongly contracting reflection laws
title Ergodic properties of polygonal billiards with strongly contracting reflection laws
spellingShingle Ergodic properties of polygonal billiards with strongly contracting reflection laws
Magno, Gianluigi Del
title_short Ergodic properties of polygonal billiards with strongly contracting reflection laws
title_full Ergodic properties of polygonal billiards with strongly contracting reflection laws
title_fullStr Ergodic properties of polygonal billiards with strongly contracting reflection laws
title_full_unstemmed Ergodic properties of polygonal billiards with strongly contracting reflection laws
title_sort Ergodic properties of polygonal billiards with strongly contracting reflection laws
author Magno, Gianluigi Del
author_facet Magno, Gianluigi Del
Dias, João Lopes
Duarte, Pedro
Gaivão, José Pedro
author_role author
author2 Dias, João Lopes
Duarte, Pedro
Gaivão, José Pedro
author2_role author
author
author
dc.contributor.none.fl_str_mv Repositório da Universidade de Lisboa
dc.contributor.author.fl_str_mv Magno, Gianluigi Del
Dias, João Lopes
Duarte, Pedro
Gaivão, José Pedro
description We consider convex polygonal billiards with a reflection law that contracts the reflection angle towards the normal. Polygonal billiards with orthogonal reflections are called slap maps. For polygons without parallel sides facing each other, the slap map has a finite number of ergodic absolutely continuous invariant probability measures. We show that any billiard with a strongly contracting reflection law has the same number of ergodic SRB measures with the same mixing periods as the ergodic absolutely continuous invariant probabilities of its corresponding slap map. The case of billiards in regular polygons and triangles is studied in detail.
publishDate 2015
dc.date.none.fl_str_mv 2015-10-02T14:00:12Z
2015
2015-01-01T00:00:00Z
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/10400.5/9286
url http://hdl.handle.net/10400.5/9286
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Magno, Gianluigi Del ... [et al.] (2015). "Ergodic properties of polygonal billiards with strongly contracting reflection laws". Instituto Superior de Economia e Gestão – CEMAPRE preprint
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 ISEG - CEMAPRE
publisher.none.fl_str_mv ISEG - CEMAPRE
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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
repository.mail.fl_str_mv
_version_ 1799131043490430976

Registros relacionados