Equilibrium states for non-uniformly hyperbolic systems: Statistical properties and analyticity
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.3934/dcds.2021045 http://hdl.handle.net/11449/206275 |
Resumo: | We consider a wide family of non-uniformly expanding maps and hyperbolic Hölder continuous potentials. We prove that the unique equilibrium state associated to each element of this family is given by the eigenfunction of the transfer operator and the eigenmeasure of the dual operator (both having the spectral radius as eigenvalue). We show that the transfer operator has the spectral gap property in some space of Hölder continuous observables and from this we obtain an exponential decay of correlations and a central limit theorem for the equilibrium state. Moreover, we establish the analyticity with respect to the potential of the equilibrium state as well as that of other thermodynamic quantities. Furthermore, we derive similar results for the equilibrium state associated to a family of non-uniformly hyperbolic skew products and hyperbolic Hölder continuous potentials. |
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Equilibrium states for non-uniformly hyperbolic systems: Statistical properties and analyticityAnalyticityEquilibrium statesLimit theoremsNon-uniform hyperbolicityPartial hyperbolicityWe consider a wide family of non-uniformly expanding maps and hyperbolic Hölder continuous potentials. We prove that the unique equilibrium state associated to each element of this family is given by the eigenfunction of the transfer operator and the eigenmeasure of the dual operator (both having the spectral radius as eigenvalue). We show that the transfer operator has the spectral gap property in some space of Hölder continuous observables and from this we obtain an exponential decay of correlations and a central limit theorem for the equilibrium state. Moreover, we establish the analyticity with respect to the potential of the equilibrium state as well as that of other thermodynamic quantities. Furthermore, we derive similar results for the equilibrium state associated to a family of non-uniformly hyperbolic skew products and hyperbolic Hölder continuous potentials.Universidade Estadual Paulista (UNESP) Instituto de Geociências e Ciências Exatas, Câmpus de Rio Claro Avenida 24-A, 1515, Bela Vista, Rio ClaroCentro de Ciências Exatas e Tecnologia-Ufma, Av. dos Portugueses, 1966Instituto de Matemática Universidade Federal Do Rio de Janeiro, Av. Athos da Silveira Ramos 149, Cidade Universitária Ilha do FundaõUniversidade Estadual Paulista (UNESP) Instituto de Geociências e Ciências Exatas, Câmpus de Rio Claro Avenida 24-A, 1515, Bela Vista, Rio ClaroUniversidade Estadual Paulista (Unesp)Centro de Ciências Exatas e Tecnologia-UfmaUniversidade Federal do Rio de Janeiro (UFRJ)Afonso, Suzete Maria [UNESP]Ramos, VanessaSiqueira, Jaqueline2021-06-25T10:29:23Z2021-06-25T10:29:23Z2021-09-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article4488-4513http://dx.doi.org/10.3934/dcds.2021045Discrete and Continuous Dynamical Systems- Series A, v. 41, n. 9, p. 4488-4513, 2021.1553-52311078-0947http://hdl.handle.net/11449/20627510.3934/dcds.20210452-s2.0-85105081971Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengDiscrete and Continuous Dynamical Systems- Series Ainfo:eu-repo/semantics/openAccess2021-10-23T02:54:18Zoai:repositorio.unesp.br:11449/206275Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T19:04:35.466105Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Equilibrium states for non-uniformly hyperbolic systems: Statistical properties and analyticity |
title |
Equilibrium states for non-uniformly hyperbolic systems: Statistical properties and analyticity |
spellingShingle |
Equilibrium states for non-uniformly hyperbolic systems: Statistical properties and analyticity Afonso, Suzete Maria [UNESP] Analyticity Equilibrium states Limit theorems Non-uniform hyperbolicity Partial hyperbolicity |
title_short |
Equilibrium states for non-uniformly hyperbolic systems: Statistical properties and analyticity |
title_full |
Equilibrium states for non-uniformly hyperbolic systems: Statistical properties and analyticity |
title_fullStr |
Equilibrium states for non-uniformly hyperbolic systems: Statistical properties and analyticity |
title_full_unstemmed |
Equilibrium states for non-uniformly hyperbolic systems: Statistical properties and analyticity |
title_sort |
Equilibrium states for non-uniformly hyperbolic systems: Statistical properties and analyticity |
author |
Afonso, Suzete Maria [UNESP] |
author_facet |
Afonso, Suzete Maria [UNESP] Ramos, Vanessa Siqueira, Jaqueline |
author_role |
author |
author2 |
Ramos, Vanessa Siqueira, Jaqueline |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Centro de Ciências Exatas e Tecnologia-Ufma Universidade Federal do Rio de Janeiro (UFRJ) |
dc.contributor.author.fl_str_mv |
Afonso, Suzete Maria [UNESP] Ramos, Vanessa Siqueira, Jaqueline |
dc.subject.por.fl_str_mv |
Analyticity Equilibrium states Limit theorems Non-uniform hyperbolicity Partial hyperbolicity |
topic |
Analyticity Equilibrium states Limit theorems Non-uniform hyperbolicity Partial hyperbolicity |
description |
We consider a wide family of non-uniformly expanding maps and hyperbolic Hölder continuous potentials. We prove that the unique equilibrium state associated to each element of this family is given by the eigenfunction of the transfer operator and the eigenmeasure of the dual operator (both having the spectral radius as eigenvalue). We show that the transfer operator has the spectral gap property in some space of Hölder continuous observables and from this we obtain an exponential decay of correlations and a central limit theorem for the equilibrium state. Moreover, we establish the analyticity with respect to the potential of the equilibrium state as well as that of other thermodynamic quantities. Furthermore, we derive similar results for the equilibrium state associated to a family of non-uniformly hyperbolic skew products and hyperbolic Hölder continuous potentials. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-06-25T10:29:23Z 2021-06-25T10:29:23Z 2021-09-01 |
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://dx.doi.org/10.3934/dcds.2021045 Discrete and Continuous Dynamical Systems- Series A, v. 41, n. 9, p. 4488-4513, 2021. 1553-5231 1078-0947 http://hdl.handle.net/11449/206275 10.3934/dcds.2021045 2-s2.0-85105081971 |
url |
http://dx.doi.org/10.3934/dcds.2021045 http://hdl.handle.net/11449/206275 |
identifier_str_mv |
Discrete and Continuous Dynamical Systems- Series A, v. 41, n. 9, p. 4488-4513, 2021. 1553-5231 1078-0947 10.3934/dcds.2021045 2-s2.0-85105081971 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Discrete and Continuous Dynamical Systems- Series A |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
4488-4513 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808129015717822464 |