On the entropy of conservative flows

Detalhes bibliográficos
Autor(a) principal: Bessa, Mário
Data de Publicação: 2010
Outros Autores: Varandas, Paulo
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.2/13882
Resumo: We obtain a C1-generic subset of the incompressible flows in a closed three-dimensional manifold where Pesin’s entropy formula holds thus establishing the continuous-time version of Tahzibi (C R Acad Sci Paris I 335:1057–1062, 2002). Moreover, in any compact manifold of dimension larger or equal to three we obtain that the metric entropy function and the integrated upper Lyapunov exponent function are not continuous with respect to the C1 Whitney topology. Finally, we establish the C2- genericity of Pesin’s entropy formula in the context of Hamiltonian four-dimensional flows.
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spelling On the entropy of conservative flowsDivergence-free vector fieldsHamiltoniansLyapunov exponentsMetric entropyWe obtain a C1-generic subset of the incompressible flows in a closed three-dimensional manifold where Pesin’s entropy formula holds thus establishing the continuous-time version of Tahzibi (C R Acad Sci Paris I 335:1057–1062, 2002). Moreover, in any compact manifold of dimension larger or equal to three we obtain that the metric entropy function and the integrated upper Lyapunov exponent function are not continuous with respect to the C1 Whitney topology. Finally, we establish the C2- genericity of Pesin’s entropy formula in the context of Hamiltonian four-dimensional flows.SpringerRepositório AbertoBessa, MárioVarandas, Paulo2023-05-29T14:50:51Z20102010-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/13882engM. Bessa, P. Varandas, On the Entropy of Conservative Flows, Qualitative Theory of Dynamical Systems, 10, 1, 11-22, 201010.1007/s12346-010-0033-6info: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:RCAAP2023-11-16T15:46:13Zoai:repositorioaberto.uab.pt:10400.2/13882Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:52:48.149474Repositório 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 the entropy of conservative flows
title On the entropy of conservative flows
spellingShingle On the entropy of conservative flows
Bessa, Mário
Divergence-free vector fields
Hamiltonians
Lyapunov exponents
Metric entropy
title_short On the entropy of conservative flows
title_full On the entropy of conservative flows
title_fullStr On the entropy of conservative flows
title_full_unstemmed On the entropy of conservative flows
title_sort On the entropy of conservative flows
author Bessa, Mário
author_facet Bessa, Mário
Varandas, Paulo
author_role author
author2 Varandas, Paulo
author2_role author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Bessa, Mário
Varandas, Paulo
dc.subject.por.fl_str_mv Divergence-free vector fields
Hamiltonians
Lyapunov exponents
Metric entropy
topic Divergence-free vector fields
Hamiltonians
Lyapunov exponents
Metric entropy
description We obtain a C1-generic subset of the incompressible flows in a closed three-dimensional manifold where Pesin’s entropy formula holds thus establishing the continuous-time version of Tahzibi (C R Acad Sci Paris I 335:1057–1062, 2002). Moreover, in any compact manifold of dimension larger or equal to three we obtain that the metric entropy function and the integrated upper Lyapunov exponent function are not continuous with respect to the C1 Whitney topology. Finally, we establish the C2- genericity of Pesin’s entropy formula in the context of Hamiltonian four-dimensional flows.
publishDate 2010
dc.date.none.fl_str_mv 2010
2010-01-01T00:00:00Z
2023-05-29T14:50:51Z
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/10400.2/13882
url http://hdl.handle.net/10400.2/13882
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv M. Bessa, P. Varandas, On the Entropy of Conservative Flows, Qualitative Theory of Dynamical Systems, 10, 1, 11-22, 2010
10.1007/s12346-010-0033-6
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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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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