Lyapunov exponents and entropy for divergence-free Lipschitz vector fields
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.2/13927 |
Resumo: | Let X^0,1( M ) be the subset of divergence-free Lipschitz vector fields defined on a closed Riemannian manifold M endowed with the Lipschitz topology ∥ · ∥_0,1 where ν is the volume measure. Let L be the subset of vector fields satisfying the L-property, a property that implies C^1-regularity ν-almost everywhere. We prove that there exists a residual subset R ⊂ L with respect to ∥·∥0,1 such that Pesin’s entropy formula holds, i.e. for any X ∈ R the metric entropy equals the integral, with respect to ν, of the sum of the positive Lyapunov exponents. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Lyapunov exponents and entropy for divergence-free Lipschitz vector fieldsVolume-preserving flowsLyapunov exponentsMetric entropyLipschitz vector fieldsLet X^0,1( M ) be the subset of divergence-free Lipschitz vector fields defined on a closed Riemannian manifold M endowed with the Lipschitz topology ∥ · ∥_0,1 where ν is the volume measure. Let L be the subset of vector fields satisfying the L-property, a property that implies C^1-regularity ν-almost everywhere. We prove that there exists a residual subset R ⊂ L with respect to ∥·∥0,1 such that Pesin’s entropy formula holds, i.e. for any X ∈ R the metric entropy equals the integral, with respect to ν, of the sum of the positive Lyapunov exponents.SpringerRepositório AbertoBessa, Mário2023-05-31T11:54:43Z20232023-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/13927engBessa, M. Lyapunov exponents and entropy for divergence-free Lipschitz vector fields. European Journal of Mathematics 9, 20 (2023)10.1007/s40879-023-00611-6info: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:RCAAP2023-11-16T15:46:07Zoai:repositorioaberto.uab.pt:10400.2/13927Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:52:45.704868Repositório 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 |
Lyapunov exponents and entropy for divergence-free Lipschitz vector fields |
title |
Lyapunov exponents and entropy for divergence-free Lipschitz vector fields |
spellingShingle |
Lyapunov exponents and entropy for divergence-free Lipschitz vector fields Bessa, Mário Volume-preserving flows Lyapunov exponents Metric entropy Lipschitz vector fields |
title_short |
Lyapunov exponents and entropy for divergence-free Lipschitz vector fields |
title_full |
Lyapunov exponents and entropy for divergence-free Lipschitz vector fields |
title_fullStr |
Lyapunov exponents and entropy for divergence-free Lipschitz vector fields |
title_full_unstemmed |
Lyapunov exponents and entropy for divergence-free Lipschitz vector fields |
title_sort |
Lyapunov exponents and entropy for divergence-free Lipschitz vector fields |
author |
Bessa, Mário |
author_facet |
Bessa, Mário |
author_role |
author |
dc.contributor.none.fl_str_mv |
Repositório Aberto |
dc.contributor.author.fl_str_mv |
Bessa, Mário |
dc.subject.por.fl_str_mv |
Volume-preserving flows Lyapunov exponents Metric entropy Lipschitz vector fields |
topic |
Volume-preserving flows Lyapunov exponents Metric entropy Lipschitz vector fields |
description |
Let X^0,1( M ) be the subset of divergence-free Lipschitz vector fields defined on a closed Riemannian manifold M endowed with the Lipschitz topology ∥ · ∥_0,1 where ν is the volume measure. Let L be the subset of vector fields satisfying the L-property, a property that implies C^1-regularity ν-almost everywhere. We prove that there exists a residual subset R ⊂ L with respect to ∥·∥0,1 such that Pesin’s entropy formula holds, i.e. for any X ∈ R the metric entropy equals the integral, with respect to ν, of the sum of the positive Lyapunov exponents. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-05-31T11:54:43Z 2023 2023-01-01T00:00:00Z |
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/10400.2/13927 |
url |
http://hdl.handle.net/10400.2/13927 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Bessa, M. Lyapunov exponents and entropy for divergence-free Lipschitz vector fields. European Journal of Mathematics 9, 20 (2023) 10.1007/s40879-023-00611-6 |
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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1799135121745379328 |