On shadowing and hyperbolicity for geodesic flows on surfaces

Detalhes bibliográficos
Autor(a) principal: Bessa, Mario
Data de Publicação: 2017
Outros Autores: Dias, João Lopes, Torres, Maria Joana
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.6/9019
Resumo: We prove that the geodesic flow on closed surfaces displays a hyperbolic set if the shadowing property holds C2-robustly on the metric. Similar results are obtained when considering even feeble properties like the weak shadowing and the specification properties. Despite the Hamiltonian nature of the geodesic flow, the arguments in the present paper differ completely from those used in Bessa et al. (2013) for Hamiltonian systems.
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spelling On shadowing and hyperbolicity for geodesic flows on surfacesGeodesic flowHyperbolic setsShadowingSpecificationWe prove that the geodesic flow on closed surfaces displays a hyperbolic set if the shadowing property holds C2-robustly on the metric. Similar results are obtained when considering even feeble properties like the weak shadowing and the specification properties. Despite the Hamiltonian nature of the geodesic flow, the arguments in the present paper differ completely from those used in Bessa et al. (2013) for Hamiltonian systems.uBibliorumBessa, MarioDias, João LopesTorres, Maria Joana2020-02-05T09:54:55Z20172017-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.6/9019enghttp://dx.doi.org/10.1016/j.na.2017.02.006metadata only accessinfo: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:RCAAP2023-12-15T09:49:36Zoai:ubibliorum.ubi.pt:10400.6/9019Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:49:16.461592Repositório 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 On shadowing and hyperbolicity for geodesic flows on surfaces
title On shadowing and hyperbolicity for geodesic flows on surfaces
spellingShingle On shadowing and hyperbolicity for geodesic flows on surfaces
Bessa, Mario
Geodesic flow
Hyperbolic sets
Shadowing
Specification
title_short On shadowing and hyperbolicity for geodesic flows on surfaces
title_full On shadowing and hyperbolicity for geodesic flows on surfaces
title_fullStr On shadowing and hyperbolicity for geodesic flows on surfaces
title_full_unstemmed On shadowing and hyperbolicity for geodesic flows on surfaces
title_sort On shadowing and hyperbolicity for geodesic flows on surfaces
author Bessa, Mario
author_facet Bessa, Mario
Dias, João Lopes
Torres, Maria Joana
author_role author
author2 Dias, João Lopes
Torres, Maria Joana
author2_role author
author
dc.contributor.none.fl_str_mv uBibliorum
dc.contributor.author.fl_str_mv Bessa, Mario
Dias, João Lopes
Torres, Maria Joana
dc.subject.por.fl_str_mv Geodesic flow
Hyperbolic sets
Shadowing
Specification
topic Geodesic flow
Hyperbolic sets
Shadowing
Specification
description We prove that the geodesic flow on closed surfaces displays a hyperbolic set if the shadowing property holds C2-robustly on the metric. Similar results are obtained when considering even feeble properties like the weak shadowing and the specification properties. Despite the Hamiltonian nature of the geodesic flow, the arguments in the present paper differ completely from those used in Bessa et al. (2013) for Hamiltonian systems.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-01-01T00:00:00Z
2020-02-05T09:54:55Z
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dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.6/9019
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dc.language.iso.fl_str_mv eng
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