There are no proper topological hyperbolic homoclinic classes for area-preserving maps

Detalhes bibliográficos
Autor(a) principal: Bessa, Mário
Data de Publicação: 2020
Outros Autores: Torres, M. J.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/64189
Resumo: We begin by defining a homoclinic class for homeomorphisms. Then we prove that if a topological homoclinic class \Lambda associated to an area-preserving homeomorphism f on a surface M is topologically hyperbolic (i.e. has the shadowing and expansiveness properties), then \Lambda=M and f is an Anosov homeomorphism.
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spelling There are no proper topological hyperbolic homoclinic classes for area-preserving mapsShadowingExpansivenessTopological dynamicsHomoclinic classesCiências Naturais::MatemáticasScience & TechnologyWe begin by defining a homoclinic class for homeomorphisms. Then we prove that if a topological homoclinic class \Lambda associated to an area-preserving homeomorphism f on a surface M is topologically hyperbolic (i.e. has the shadowing and expansiveness properties), then \Lambda=M and f is an Anosov homeomorphism.MB was partially supported by FCT - ‘Fundação para a Ciência e a Tecnologia’, through Centro de Matemática e Aplicações (CMA-UBI), Universidade da Beira Interior, project UID/MAT/00212/2013. MJT was partially supported by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the ‘Fundação para a Ciência e a Tecnologia’, through the Project UID/MAT/00013/2013.Cambridge University PressUniversidade do MinhoBessa, MárioTorres, M. J.20202020-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/64189eng0013-09151464-383910.1017/S0013091519000282https://www.cambridge.org/core/journals/proceedings-of-the-edinburgh-mathematical-society/article/there-are-no-proper-topological-hyperbolic-homoclinic-classes-for-areapreserving-maps/4232BAC3B800704E53605E9CAF044072info: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:RCAAP2023-07-21T12:49:55Zoai:repositorium.sdum.uminho.pt:1822/64189Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:48:31.285191Repositório 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 There are no proper topological hyperbolic homoclinic classes for area-preserving maps
title There are no proper topological hyperbolic homoclinic classes for area-preserving maps
spellingShingle There are no proper topological hyperbolic homoclinic classes for area-preserving maps
Bessa, Mário
Shadowing
Expansiveness
Topological dynamics
Homoclinic classes
Ciências Naturais::Matemáticas
Science & Technology
title_short There are no proper topological hyperbolic homoclinic classes for area-preserving maps
title_full There are no proper topological hyperbolic homoclinic classes for area-preserving maps
title_fullStr There are no proper topological hyperbolic homoclinic classes for area-preserving maps
title_full_unstemmed There are no proper topological hyperbolic homoclinic classes for area-preserving maps
title_sort There are no proper topological hyperbolic homoclinic classes for area-preserving maps
author Bessa, Mário
author_facet Bessa, Mário
Torres, M. J.
author_role author
author2 Torres, M. J.
author2_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Bessa, Mário
Torres, M. J.
dc.subject.por.fl_str_mv Shadowing
Expansiveness
Topological dynamics
Homoclinic classes
Ciências Naturais::Matemáticas
Science & Technology
topic Shadowing
Expansiveness
Topological dynamics
Homoclinic classes
Ciências Naturais::Matemáticas
Science & Technology
description We begin by defining a homoclinic class for homeomorphisms. Then we prove that if a topological homoclinic class \Lambda associated to an area-preserving homeomorphism f on a surface M is topologically hyperbolic (i.e. has the shadowing and expansiveness properties), then \Lambda=M and f is an Anosov homeomorphism.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-01-01T00:00:00Z
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/1822/64189
url http://hdl.handle.net/1822/64189
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0013-0915
1464-3839
10.1017/S0013091519000282
https://www.cambridge.org/core/journals/proceedings-of-the-edinburgh-mathematical-society/article/there-are-no-proper-topological-hyperbolic-homoclinic-classes-for-areapreserving-maps/4232BAC3B800704E53605E9CAF044072
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 Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
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
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