Trivial and simple spectrum for SL(d, ℝ) cocycles with free base and fiber dynamics

Detalhes bibliográficos
Autor(a) principal: Bessa, Mário
Data de Publicação: 2015
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/10400.2/13898
Resumo: Let AC_D(M,SL(d,R)) denote the pairs (f,A) so that f ∈ A ⊂ Diff (M) is a C^1-Anosov transitive diffeomorphisms and A is an SL(d,R) cocycle dominated with respect to f. We prove that open and densely in AC_D(M,SL(d,R)), in appropriate topologies, the pair (f,A) has simple spectrum with respect to the unique maximal entropy measure μ_f. Then, we prove prevalence of trivial spectrum near the dynamical cocycle of an area-preserving map and also for generic cocycles in Aut_Leb(M) × Lp(M,SL(d,R)).
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spelling Trivial and simple spectrum for SL(d, ℝ) cocycles with free base and fiber dynamicsLinear cocyclesLyapunov exponentsAnosov diffeomorphismsTopological conjugacyMaximal entropy measuresLet AC_D(M,SL(d,R)) denote the pairs (f,A) so that f ∈ A ⊂ Diff (M) is a C^1-Anosov transitive diffeomorphisms and A is an SL(d,R) cocycle dominated with respect to f. We prove that open and densely in AC_D(M,SL(d,R)), in appropriate topologies, the pair (f,A) has simple spectrum with respect to the unique maximal entropy measure μ_f. Then, we prove prevalence of trivial spectrum near the dynamical cocycle of an area-preserving map and also for generic cocycles in Aut_Leb(M) × Lp(M,SL(d,R)).SpringerRepositório AbertoBessa, MárioVarandas, Paulo2023-05-30T10:31:26Z20152015-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/13898engBessa, M., Varandas, P. Trivial and simple spectrum for SL(d, ℝ) cocycles with free base and fiber dynamics. Acta. Math. Sin.-English Ser. 31, 1113–1122 (2015)10.1007/s10114-015-4417-zinfo: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:10400.2/13898Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:52:46.151539Repositório 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 Trivial and simple spectrum for SL(d, ℝ) cocycles with free base and fiber dynamics
title Trivial and simple spectrum for SL(d, ℝ) cocycles with free base and fiber dynamics
spellingShingle Trivial and simple spectrum for SL(d, ℝ) cocycles with free base and fiber dynamics
Bessa, Mário
Linear cocycles
Lyapunov exponents
Anosov diffeomorphisms
Topological conjugacy
Maximal entropy measures
title_short Trivial and simple spectrum for SL(d, ℝ) cocycles with free base and fiber dynamics
title_full Trivial and simple spectrum for SL(d, ℝ) cocycles with free base and fiber dynamics
title_fullStr Trivial and simple spectrum for SL(d, ℝ) cocycles with free base and fiber dynamics
title_full_unstemmed Trivial and simple spectrum for SL(d, ℝ) cocycles with free base and fiber dynamics
title_sort Trivial and simple spectrum for SL(d, ℝ) cocycles with free base and fiber dynamics
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 Linear cocycles
Lyapunov exponents
Anosov diffeomorphisms
Topological conjugacy
Maximal entropy measures
topic Linear cocycles
Lyapunov exponents
Anosov diffeomorphisms
Topological conjugacy
Maximal entropy measures
description Let AC_D(M,SL(d,R)) denote the pairs (f,A) so that f ∈ A ⊂ Diff (M) is a C^1-Anosov transitive diffeomorphisms and A is an SL(d,R) cocycle dominated with respect to f. We prove that open and densely in AC_D(M,SL(d,R)), in appropriate topologies, the pair (f,A) has simple spectrum with respect to the unique maximal entropy measure μ_f. Then, we prove prevalence of trivial spectrum near the dynamical cocycle of an area-preserving map and also for generic cocycles in Aut_Leb(M) × Lp(M,SL(d,R)).
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-01-01T00:00:00Z
2023-05-30T10:31:26Z
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/10400.2/13898
url http://hdl.handle.net/10400.2/13898
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Bessa, M., Varandas, P. Trivial and simple spectrum for SL(d, ℝ) cocycles with free base and fiber dynamics. Acta. Math. Sin.-English Ser. 31, 1113–1122 (2015)
10.1007/s10114-015-4417-z
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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