A dichotomy in area-preserving reversible maps

Detalhes bibliográficos
Autor(a) principal: Bessa, Mário
Data de Publicação: 2015
Outros Autores: Rodrigues, Alexandre A. P.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.2/13895
Resumo: In this paper we study R-reversible area-preserving maps f : M → M on a two-dimensional Riemannian closed manifold M, i.e. diffeomorphisms f such that R ◦ f = f−1 ◦ R where R: M → M is an isometric involution. We obtain a C1-residual subset where any map inside it is Anosov or else has a dense set of elliptic periodic orbits, thus establishing the stability conjecture in this setting. Along the paper we derive the C1-Closing Lemma for reversible maps and other perturbation toolboxes.
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spelling A dichotomy in area-preserving reversible mapsReversing symmetryArea-preserving mapClosing LemmaElliptic pointIn this paper we study R-reversible area-preserving maps f : M → M on a two-dimensional Riemannian closed manifold M, i.e. diffeomorphisms f such that R ◦ f = f−1 ◦ R where R: M → M is an isometric involution. We obtain a C1-residual subset where any map inside it is Anosov or else has a dense set of elliptic periodic orbits, thus establishing the stability conjecture in this setting. Along the paper we derive the C1-Closing Lemma for reversible maps and other perturbation toolboxes.SpringerRepositório AbertoBessa, MárioRodrigues, Alexandre A. P.2023-05-30T08:58:03Z20152015-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/13895engBessa, M., Rodrigues, A.A.P. A Dichotomy in Area-Preserving Reversible Maps. Qual. Theory Dyn. Syst. 15, 309–326 (2016).10.1007/s12346-015-0155-yinfo: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:RCAAP2023-11-16T15:46:14Zoai:repositorioaberto.uab.pt:10400.2/13895Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:52:48.232473Repositório 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 A dichotomy in area-preserving reversible maps
title A dichotomy in area-preserving reversible maps
spellingShingle A dichotomy in area-preserving reversible maps
Bessa, Mário
Reversing symmetry
Area-preserving map
Closing Lemma
Elliptic point
title_short A dichotomy in area-preserving reversible maps
title_full A dichotomy in area-preserving reversible maps
title_fullStr A dichotomy in area-preserving reversible maps
title_full_unstemmed A dichotomy in area-preserving reversible maps
title_sort A dichotomy in area-preserving reversible maps
author Bessa, Mário
author_facet Bessa, Mário
Rodrigues, Alexandre A. P.
author_role author
author2 Rodrigues, Alexandre A. P.
author2_role author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Bessa, Mário
Rodrigues, Alexandre A. P.
dc.subject.por.fl_str_mv Reversing symmetry
Area-preserving map
Closing Lemma
Elliptic point
topic Reversing symmetry
Area-preserving map
Closing Lemma
Elliptic point
description In this paper we study R-reversible area-preserving maps f : M → M on a two-dimensional Riemannian closed manifold M, i.e. diffeomorphisms f such that R ◦ f = f−1 ◦ R where R: M → M is an isometric involution. We obtain a C1-residual subset where any map inside it is Anosov or else has a dense set of elliptic periodic orbits, thus establishing the stability conjecture in this setting. Along the paper we derive the C1-Closing Lemma for reversible maps and other perturbation toolboxes.
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-01-01T00:00:00Z
2023-05-30T08:58:03Z
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/10400.2/13895
url http://hdl.handle.net/10400.2/13895
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Bessa, M., Rodrigues, A.A.P. A Dichotomy in Area-Preserving Reversible Maps. Qual. Theory Dyn. Syst. 15, 309–326 (2016).
10.1007/s12346-015-0155-y
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 Springer
publisher.none.fl_str_mv Springer
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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