Ergodicity in Umbrella Billiards
Autor(a) principal: | |
---|---|
Data de Publicação: | 2017 |
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/10174/21898 https://doi.org/https://dx.doi.org/10.22606/nhmp.2017.12004 |
Resumo: | We investigate a three-parameter family of billiard tables with circular arc boundaries. These umbrella-shaped billiards may be viewed as a generalization of two-parameter moon and asymmetric lemon billiards, in which the latter classes comprise instances where the new parameter is 0. Like those two previously studied classes, for certain parameters umbrella billiards exhibit evidence of chaotic behavior despite failing to meet certain criteria for defocusing or dispersing, the two most well understood mechanisms for generating ergodicity and hyperbolicity. For some parameters corresponding to non-ergodic lemon and moon billiards, small increases in the new parameter transform elliptic 2-periodic points into a cascade of higher order elliptic points. These may either stabilize or dissipate as the new parameter is increased. We characterize the periodic points and present evidence of new ergodic examples. |
id |
RCAP_355a3b8bfc60a802b17711d519082ee9 |
---|---|
oai_identifier_str |
oai:dspace.uevora.pt:10174/21898 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
Ergodicity in Umbrella BilliardsErgodicitybilliard systemsperiodic pointselliptic islandsWe investigate a three-parameter family of billiard tables with circular arc boundaries. These umbrella-shaped billiards may be viewed as a generalization of two-parameter moon and asymmetric lemon billiards, in which the latter classes comprise instances where the new parameter is 0. Like those two previously studied classes, for certain parameters umbrella billiards exhibit evidence of chaotic behavior despite failing to meet certain criteria for defocusing or dispersing, the two most well understood mechanisms for generating ergodicity and hyperbolicity. For some parameters corresponding to non-ergodic lemon and moon billiards, small increases in the new parameter transform elliptic 2-periodic points into a cascade of higher order elliptic points. These may either stabilize or dissipate as the new parameter is increased. We characterize the periodic points and present evidence of new ergodic examples.Isaac Scientific Publishing2018-01-23T10:22:35Z2018-01-232017-09-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10174/21898https://doi.org/https://dx.doi.org/10.22606/nhmp.2017.12004http://hdl.handle.net/10174/21898https://doi.org/https://dx.doi.org/10.22606/nhmp.2017.12004engM.Correia, C.Cox, H.-K.Zhang (2017) Ergodicity in Umbrella Billiards. New Horizons in Mathematical Physics, Vol.1, No.2ISSN:2521-7402mfac@uevora.ptclcox@wustl.eduhongkun@math.umass.edu721Correia, MariaCox, ChristopherZhang, Hong-Kuninfo: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:RCAAP2024-01-03T19:12:19Zoai:dspace.uevora.pt:10174/21898Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:12:50.369263Repositório 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 |
Ergodicity in Umbrella Billiards |
title |
Ergodicity in Umbrella Billiards |
spellingShingle |
Ergodicity in Umbrella Billiards Correia, Maria Ergodicity billiard systems periodic points elliptic islands |
title_short |
Ergodicity in Umbrella Billiards |
title_full |
Ergodicity in Umbrella Billiards |
title_fullStr |
Ergodicity in Umbrella Billiards |
title_full_unstemmed |
Ergodicity in Umbrella Billiards |
title_sort |
Ergodicity in Umbrella Billiards |
author |
Correia, Maria |
author_facet |
Correia, Maria Cox, Christopher Zhang, Hong-Kun |
author_role |
author |
author2 |
Cox, Christopher Zhang, Hong-Kun |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Correia, Maria Cox, Christopher Zhang, Hong-Kun |
dc.subject.por.fl_str_mv |
Ergodicity billiard systems periodic points elliptic islands |
topic |
Ergodicity billiard systems periodic points elliptic islands |
description |
We investigate a three-parameter family of billiard tables with circular arc boundaries. These umbrella-shaped billiards may be viewed as a generalization of two-parameter moon and asymmetric lemon billiards, in which the latter classes comprise instances where the new parameter is 0. Like those two previously studied classes, for certain parameters umbrella billiards exhibit evidence of chaotic behavior despite failing to meet certain criteria for defocusing or dispersing, the two most well understood mechanisms for generating ergodicity and hyperbolicity. For some parameters corresponding to non-ergodic lemon and moon billiards, small increases in the new parameter transform elliptic 2-periodic points into a cascade of higher order elliptic points. These may either stabilize or dissipate as the new parameter is increased. We characterize the periodic points and present evidence of new ergodic examples. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-09-01T00:00:00Z 2018-01-23T10:22:35Z 2018-01-23 |
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/10174/21898 https://doi.org/https://dx.doi.org/10.22606/nhmp.2017.12004 http://hdl.handle.net/10174/21898 https://doi.org/https://dx.doi.org/10.22606/nhmp.2017.12004 |
url |
http://hdl.handle.net/10174/21898 https://doi.org/https://dx.doi.org/10.22606/nhmp.2017.12004 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
M.Correia, C.Cox, H.-K.Zhang (2017) Ergodicity in Umbrella Billiards. New Horizons in Mathematical Physics, Vol.1, No.2 ISSN:2521-7402 mfac@uevora.pt clcox@wustl.edu hongkun@math.umass.edu 721 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Isaac Scientific Publishing |
publisher.none.fl_str_mv |
Isaac Scientific Publishing |
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_ |
1799136610139242496 |