Ergodic properties of polygonal billiards with strongly contracting reflection laws
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Outros Autores: | , , |
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. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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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 |
|
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1799131043490430976 |