Livschitz Theorem in suspension flows and Markov systems: approach in cohomology of systems

Detalhes bibliográficos
Autor(a) principal: Laureano, R. D.
Data de Publicação: 2020
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10071/20401
Resumo: It is presented and proved a version of Livschitz Theorem for hyperbolic flows pragmatically oriented to the cohomological context. Previously, it is introduced the concept of cocycle and a natural notion of symmetry for cocycles. It is discussed the fundamental relationship between the existence of solutions of cohomological equations and the behavior of the cocycles along periodic orbits. The generalization of this theorem to a class of suspension flows is also discussed and proved. This generalization allows giving a different proof of the Livschitz Theorem for flows based on the construction of Markov systems for hyperbolic flows.
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spelling Livschitz Theorem in suspension flows and Markov systems: approach in cohomology of systemsCocyclesCohomological equationsAnosov Closing LemmaHyperbolic flowsLivschitz TheoremMarkov systemsSuspension flowsIt is presented and proved a version of Livschitz Theorem for hyperbolic flows pragmatically oriented to the cohomological context. Previously, it is introduced the concept of cocycle and a natural notion of symmetry for cocycles. It is discussed the fundamental relationship between the existence of solutions of cohomological equations and the behavior of the cocycles along periodic orbits. The generalization of this theorem to a class of suspension flows is also discussed and proved. This generalization allows giving a different proof of the Livschitz Theorem for flows based on the construction of Markov systems for hyperbolic flows.MDPI2020-04-22T10:55:11Z2020-01-01T00:00:00Z20202020-04-22T11:53:42Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10071/20401eng2073-899410.3390/sym12030338Laureano, R. D.info: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:RCAAP2023-11-09T17:39:41Zoai:repositorio.iscte-iul.pt:10071/20401Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:18:15.066623Repositório 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 Livschitz Theorem in suspension flows and Markov systems: approach in cohomology of systems
title Livschitz Theorem in suspension flows and Markov systems: approach in cohomology of systems
spellingShingle Livschitz Theorem in suspension flows and Markov systems: approach in cohomology of systems
Laureano, R. D.
Cocycles
Cohomological equations
Anosov Closing Lemma
Hyperbolic flows
Livschitz Theorem
Markov systems
Suspension flows
title_short Livschitz Theorem in suspension flows and Markov systems: approach in cohomology of systems
title_full Livschitz Theorem in suspension flows and Markov systems: approach in cohomology of systems
title_fullStr Livschitz Theorem in suspension flows and Markov systems: approach in cohomology of systems
title_full_unstemmed Livschitz Theorem in suspension flows and Markov systems: approach in cohomology of systems
title_sort Livschitz Theorem in suspension flows and Markov systems: approach in cohomology of systems
author Laureano, R. D.
author_facet Laureano, R. D.
author_role author
dc.contributor.author.fl_str_mv Laureano, R. D.
dc.subject.por.fl_str_mv Cocycles
Cohomological equations
Anosov Closing Lemma
Hyperbolic flows
Livschitz Theorem
Markov systems
Suspension flows
topic Cocycles
Cohomological equations
Anosov Closing Lemma
Hyperbolic flows
Livschitz Theorem
Markov systems
Suspension flows
description It is presented and proved a version of Livschitz Theorem for hyperbolic flows pragmatically oriented to the cohomological context. Previously, it is introduced the concept of cocycle and a natural notion of symmetry for cocycles. It is discussed the fundamental relationship between the existence of solutions of cohomological equations and the behavior of the cocycles along periodic orbits. The generalization of this theorem to a class of suspension flows is also discussed and proved. This generalization allows giving a different proof of the Livschitz Theorem for flows based on the construction of Markov systems for hyperbolic flows.
publishDate 2020
dc.date.none.fl_str_mv 2020-04-22T10:55:11Z
2020-01-01T00:00:00Z
2020
2020-04-22T11:53:42Z
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/10071/20401
url http://hdl.handle.net/10071/20401
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2073-8994
10.3390/sym12030338
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 MDPI
publisher.none.fl_str_mv MDPI
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
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