Stable weakly shadowable volume-preserving systems are volume-hyperbolic
Autor(a) principal: | |
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Data de Publicação: | 2014 |
Outros Autores: | , |
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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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) 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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1799135121747476480 |