Stable weakly shadowable volume-preserving systems are volume-hyperbolic

Detalhes bibliográficos
Autor(a) principal: Bessa, Mário
Data de Publicação: 2014
Outros Autores: Lee, Manseob, Vaz, Sandra
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.2/13900
Resumo: We prove that any C^1-stable weakly shadowable volume-preserving diffeomorphism defined on a compact manifold displays a dominated splitting E ⊕ F . Moreover, both E and F are volume-hyperbolic. Finally, we prove the version of this result for divergence-free vector fields. As a consequence, in low dimensions, we obtain global hyperbolicity.
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spelling Stable weakly shadowable volume-preserving systems are volume-hyperbolicWeak shadowingDominated splittingHyperbolicityWe prove that any C^1-stable weakly shadowable volume-preserving diffeomorphism defined on a compact manifold displays a dominated splitting E ⊕ F . Moreover, both E and F are volume-hyperbolic. Finally, we prove the version of this result for divergence-free vector fields. As a consequence, in low dimensions, we obtain global hyperbolicity.SpringerRepositório AbertoBessa, MárioLee, ManseobVaz, Sandra2023-05-30T10:46:59Z20142014-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/13900engBessa, M., Lee, M. & Vaz, S. Stable weakly shadowable volume-preserving systems are volume-hyperbolic. Acta. Math. Sin.-English Ser. 30, 1007–1020 (2014)10.1007/s10114-014-3093-8info: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:RCAAP2023-11-16T15:46:08Zoai:repositorioaberto.uab.pt:10400.2/13900Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:52:46.107225Repositório 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 Stable weakly shadowable volume-preserving systems are volume-hyperbolic
title Stable weakly shadowable volume-preserving systems are volume-hyperbolic
spellingShingle Stable weakly shadowable volume-preserving systems are volume-hyperbolic
Bessa, Mário
Weak shadowing
Dominated splitting
Hyperbolicity
title_short Stable weakly shadowable volume-preserving systems are volume-hyperbolic
title_full Stable weakly shadowable volume-preserving systems are volume-hyperbolic
title_fullStr Stable weakly shadowable volume-preserving systems are volume-hyperbolic
title_full_unstemmed Stable weakly shadowable volume-preserving systems are volume-hyperbolic
title_sort Stable weakly shadowable volume-preserving systems are volume-hyperbolic
author Bessa, Mário
author_facet Bessa, Mário
Lee, Manseob
Vaz, Sandra
author_role author
author2 Lee, Manseob
Vaz, Sandra
author2_role author
author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Bessa, Mário
Lee, Manseob
Vaz, Sandra
dc.subject.por.fl_str_mv Weak shadowing
Dominated splitting
Hyperbolicity
topic Weak shadowing
Dominated splitting
Hyperbolicity
description We prove that any C^1-stable weakly shadowable volume-preserving diffeomorphism defined on a compact manifold displays a dominated splitting E ⊕ F . Moreover, both E and F are volume-hyperbolic. Finally, we prove the version of this result for divergence-free vector fields. As a consequence, in low dimensions, we obtain global hyperbolicity.
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-01-01T00:00:00Z
2023-05-30T10:46:59Z
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/10400.2/13900
url http://hdl.handle.net/10400.2/13900
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Bessa, M., Lee, M. & Vaz, S. Stable weakly shadowable volume-preserving systems are volume-hyperbolic. Acta. Math. Sin.-English Ser. 30, 1007–1020 (2014)
10.1007/s10114-014-3093-8
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)
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instacron_str RCAAP
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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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