Lyapunov exponents and entropy for divergence-free Lipschitz vector fields

Detalhes bibliográficos
Autor(a) principal: Bessa, Mário
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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spelling 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)
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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
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