Chaos in the square billiard with a modified reflection law

Detalhes bibliográficos
Autor(a) principal: Del Magno, Gianluigi
Data de Publicação: 2012
Outros Autores: Dias, João Lopes, Duarte, Pedro, Gaivão, José Pedro, Pinheiro, Diogo
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.5/28949
Resumo: The purpose of this paper is to study the dynamics of a square billiard with a non-standard reflection law such that the angle of reflection of the particle is a linear contraction of the angle of incidence. We present numerical and analytical arguments that the nonwandering set of this billiard decomposes into three invariant sets, a parabolic attractor, a chaotic attractor, and a set consisting of several horseshoes. This scenario implies the positivity of the topological entropy of the billiard, a property that is in sharp contrast with the integrability of the square billiard with the standard reflection law.
id RCAP_bf302d073f5bde45d79b336037c0f4ed
oai_identifier_str oai:www.repository.utl.pt:10400.5/28949
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling Chaos in the square billiard with a modified reflection lawBilliard MapReflection LawHyperbolicityAttractors and HorseshoesThe purpose of this paper is to study the dynamics of a square billiard with a non-standard reflection law such that the angle of reflection of the particle is a linear contraction of the angle of incidence. We present numerical and analytical arguments that the nonwandering set of this billiard decomposes into three invariant sets, a parabolic attractor, a chaotic attractor, and a set consisting of several horseshoes. This scenario implies the positivity of the topological entropy of the billiard, a property that is in sharp contrast with the integrability of the square billiard with the standard reflection law.American Institute of PhysicsRepositório da Universidade de LisboaDel Magno, GianluigiDias, João LopesDuarte, PedroGaivão, José PedroPinheiro, Diogo2023-10-10T15:19:00Z20122012-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/28949engDel Magno, Gianluigi … [et al.] .(2012). "Chaos in the square billiard with a modified reflection law." Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 22, No. 2: 026106. (Search PDF in 2023)doi.org/10.1063/1.37019921089-7682info: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:RCAAP2023-10-15T01:33:02Zoai:www.repository.utl.pt:10400.5/28949Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:35:43.451044Repositório 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 Chaos in the square billiard with a modified reflection law
title Chaos in the square billiard with a modified reflection law
spellingShingle Chaos in the square billiard with a modified reflection law
Del Magno, Gianluigi
Billiard Map
Reflection Law
Hyperbolicity
Attractors and Horseshoes
title_short Chaos in the square billiard with a modified reflection law
title_full Chaos in the square billiard with a modified reflection law
title_fullStr Chaos in the square billiard with a modified reflection law
title_full_unstemmed Chaos in the square billiard with a modified reflection law
title_sort Chaos in the square billiard with a modified reflection law
author Del Magno, Gianluigi
author_facet Del Magno, Gianluigi
Dias, João Lopes
Duarte, Pedro
Gaivão, José Pedro
Pinheiro, Diogo
author_role author
author2 Dias, João Lopes
Duarte, Pedro
Gaivão, José Pedro
Pinheiro, Diogo
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Repositório da Universidade de Lisboa
dc.contributor.author.fl_str_mv Del Magno, Gianluigi
Dias, João Lopes
Duarte, Pedro
Gaivão, José Pedro
Pinheiro, Diogo
dc.subject.por.fl_str_mv Billiard Map
Reflection Law
Hyperbolicity
Attractors and Horseshoes
topic Billiard Map
Reflection Law
Hyperbolicity
Attractors and Horseshoes
description The purpose of this paper is to study the dynamics of a square billiard with a non-standard reflection law such that the angle of reflection of the particle is a linear contraction of the angle of incidence. We present numerical and analytical arguments that the nonwandering set of this billiard decomposes into three invariant sets, a parabolic attractor, a chaotic attractor, and a set consisting of several horseshoes. This scenario implies the positivity of the topological entropy of the billiard, a property that is in sharp contrast with the integrability of the square billiard with the standard reflection law.
publishDate 2012
dc.date.none.fl_str_mv 2012
2012-01-01T00:00:00Z
2023-10-10T15:19:00Z
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/10400.5/28949
url http://hdl.handle.net/10400.5/28949
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Del Magno, Gianluigi … [et al.] .(2012). "Chaos in the square billiard with a modified reflection law." Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 22, No. 2: 026106. (Search PDF in 2023)
doi.org/10.1063/1.3701992
1089-7682
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 American Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
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_ 1799133620519043072

Registros relacionados