Contributions to phase transition of intermittent skew-product and piecewise monotone dynamics on the circle
Ano de defesa: | 2023 |
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Autor(a) principal: | |
Orientador(a): | |
Banca de defesa: | , , , , |
Tipo de documento: | Tese |
Tipo de acesso: | Acesso aberto |
Idioma: | eng |
Instituição de defesa: |
Universidade Federal da Bahia
|
Programa de Pós-Graduação: |
Pós-Graduação em Matemática (PGMAT)
|
Departamento: |
Instituto de Matemática
|
País: |
Brasil
|
Palavras-chave em Português: | |
Área do conhecimento CNPq: | |
Link de acesso: | https://repositorio.ufba.br/handle/ri/38509 |
Resumo: | It is known that any uniformly dusty or hyperbolic transitive dynamics do not it has phase transition with respect to the continuous Hölder potentials. When it comes to more general dynamics, it is still an open question to classify all the dynamics that They have transition with respect to a certain class of regular potentials. In dimension 1, according to Bomfim-Carneiro [BC21], every local C1+α-diffeomorphism in the transitive circle that is neither expander nor invertible has a single thermodynamic phase transition with respect to the geometric potential, in other words, the topological pressure function R ∋ t 7→ Ptop(f, −tlog |Df|) is analytic except at a point t0 ∈ (0, 1). They also proved spectral phase transition, i.e., the transfer operator Lf,−tlog |Df| Acting in the space of continuous Hölder functions, there is a spectral gap for all t < t0 and There is no spectral gap for T ≥ T0. Our goal is to prove similar results for two special classes of dynamics: partially codimensional 1 endomorphisms hyperbolic and monotonous dynamics by parts in the circle transitive. For high-dimensional endomorphisms, we proved that the thermodynamic and spectral phase transition results imply multifractal analysis for the Lyapunov spectrum. In particular We exhibit a class of partially hyperbolic endomorphisms that admit transition of thermodynamic and spectral phase with respect to the geometric potential in the central direction, and we describe multifractal analysis of the central Lyapunov exponents. For monotonous dynamics by parts in the circle, we prove that the set of continuous Hölder potentials that do not have thermodynamic and spectral phase transition is dense in the uniform topology and the set of continuous Hölder potentials that have phase transition is not dense in the uniform topology. We also get a transitional characterization in terms of the transfer operator and the convexity type of the topological pressure function. In In particular, we describe the behavior of the topological pressure function and the associated transfer. |
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2023-11-20T12:16:20Z2023-11-20T12:16:20Z2023-03-07SILVA, Afonso Fernandes da. Contributions to phase transition of intermittent skew-product and piecewise monotone dynamics on the circle: a method for assessing quality attributes in self-adaptive systems. 2023. 79 f. Tese (Doutorado em Matemática) Instituto de Matemática e Estatística, Universidade Federal da Bahia, Salvador, Ba, 2023.https://repositorio.ufba.br/handle/ri/38509It is known that any uniformly dusty or hyperbolic transitive dynamics do not it has phase transition with respect to the continuous Hölder potentials. When it comes to more general dynamics, it is still an open question to classify all the dynamics that They have transition with respect to a certain class of regular potentials. In dimension 1, according to Bomfim-Carneiro [BC21], every local C1+α-diffeomorphism in the transitive circle that is neither expander nor invertible has a single thermodynamic phase transition with respect to the geometric potential, in other words, the topological pressure function R ∋ t 7→ Ptop(f, −tlog |Df|) is analytic except at a point t0 ∈ (0, 1). They also proved spectral phase transition, i.e., the transfer operator Lf,−tlog |Df| Acting in the space of continuous Hölder functions, there is a spectral gap for all t < t0 and There is no spectral gap for T ≥ T0. Our goal is to prove similar results for two special classes of dynamics: partially codimensional 1 endomorphisms hyperbolic and monotonous dynamics by parts in the circle transitive. For high-dimensional endomorphisms, we proved that the thermodynamic and spectral phase transition results imply multifractal analysis for the Lyapunov spectrum. In particular We exhibit a class of partially hyperbolic endomorphisms that admit transition of thermodynamic and spectral phase with respect to the geometric potential in the central direction, and we describe multifractal analysis of the central Lyapunov exponents. For monotonous dynamics by parts in the circle, we prove that the set of continuous Hölder potentials that do not have thermodynamic and spectral phase transition is dense in the uniform topology and the set of continuous Hölder potentials that have phase transition is not dense in the uniform topology. We also get a transitional characterization in terms of the transfer operator and the convexity type of the topological pressure function. In In particular, we describe the behavior of the topological pressure function and the associated transfer.Sabe-se que toda dinâmica uniformemente espansora ou hiperbólica transitiva não possui transição de fase com respeito aos potenciais Hölder contínuos. Em se tratando de dinâmicas mais gerais, ainda é uma questão em aberto classificar todas as dinâmicas que possuem transição com respeito a uma certa classe de potenciais regulares. Em dimensão 1, de acordo com Bomfim-Carneiro [BC21], todo C1+α-difeomorfismo local no círculo transitivo que não é expansor nem invertível tem uma única transição de fase termodinâmica com respeito ao potencial geométrico, em outras palavras, a função pressão topológica R ∋ t 7→ Ptop(f, −tlog |Df|) é analítica exceto em um ponto t0 ∈ (0, 1]. Eles também provaram transição de fase espectral, ou seja, o operador de transferência Lf,−tlog |Df| agindo no espaço das funções hölder contínuas tem gap espectral para todo t < t0 e não apresenta gap spectral para t ≥ t0. Nosso objetivo é provar resultados similares para duas classes especiais de dinâmicas: endomorfismos de codimensão 1 parcialmente hiperbólicos e dinâmicas monótonas por partes no círculo transitivas. Para endomorfismos em dimensão alta provamos que os resultados de transição de fase termodinâmica e espectral implicam em análise multifractal para o espectro de Lyapunov. Em particular exibimos uma clase de endomorfismos parcialmente hiperbólicos que admitem transição de fase termodinâmica e espectral com relação ao potencial geométrico na direção central, e descrevemos análise multifractal dos expoente de Lyapunov central. Para dinâmicas monótonas por partes no círculo, provamos que o conjunto de potenciais Hölder contínuos que não possuem transição de fase termodinâmica e espectral é denso na topologia uniforme e o conjunto de potenciais Hölder contínuos que têm transição de fase não é denso na topologia uniforme. Também obtemos uma caracterização de transição em termos do operador de transferência e do tipo de convexidade da função pressão topológica. Em particular, descrevemos o comportamento da função pressão topológica e do operador de transferência associado.Submitted by Afonso Silva (afonso_43@hotmail.com) on 2023-11-17T19:02:58Z No. of bitstreams: 3 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Afonso Fernandes da Silva. Tese de doutorado.pdf: 1091522 bytes, checksum: f224c0c7e0c1aa1eda91008a9ce6e549 (MD5) Ata - Afonso - assinada.pdf: 757119 bytes, checksum: 33c716d10600ccad31beb752d7e71509 (MD5)Approved for entry into archive by Solange Rocha (soluny@gmail.com) on 2023-11-20T12:16:20Z (GMT) No. of bitstreams: 3 Afonso Fernandes da Silva. Tese de doutorado.pdf: 1091522 bytes, checksum: f224c0c7e0c1aa1eda91008a9ce6e549 (MD5) Ata - Afonso - assinada.pdf: 757119 bytes, checksum: 33c716d10600ccad31beb752d7e71509 (MD5) license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5)Made available in DSpace on 2023-11-20T12:16:20Z (GMT). No. of bitstreams: 3 Afonso Fernandes da Silva. Tese de doutorado.pdf: 1091522 bytes, checksum: f224c0c7e0c1aa1eda91008a9ce6e549 (MD5) Ata - Afonso - assinada.pdf: 757119 bytes, checksum: 33c716d10600ccad31beb752d7e71509 (MD5) license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Previous issue date: 2023-03-07Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)engUniversidade Federal da BahiaPós-Graduação em Matemática (PGMAT) UFBABrasilInstituto de MatemáticaAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessTransição de faseAnálise multifractalSistemas dinâmicos diferenciaisTeoria ergódicaCNPQ::CIENCIAS EXATAS E DA TERRACNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAPhase transitionMultifractal analysisDifferential dynamical systemsErgodic theoryContributions to phase transition of intermittent skew-product and piecewise monotone dynamics on the circleContribuições para a transição de fase de skew-product intermitente e dinâmicas monótonas por partes no círculoDoutoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/publishedVersionNunes, Thiago Bomfim São Luiz0000-0003-3120-2169http://lattes.cnpq.br/8997137904643903Nunes, Thiago Bomfim São Luiz0000-0003-3120-2169http://lattes.cnpq.br/8997137904643903Araujo, Vitor Domingos Martins dehttp://lattes.cnpq.br/4817632811350748Varandas, Paulo Cesar Rodrigues Pinto0000-0002-0902-8718http://lattes.cnpq.br/1450367699820349Cruz, Anderson Reis da0000-0001-7928-4891http://lattes.cnpq.br/8911485243130142Bortolotti, Ricardo Turollahttp://lattes.cnpq.br/5596171733972807https://lattes.cnpq.br/0025628612607760Silva, Afonso Fernandes dareponame:Repositório Institucional da UFBAinstname:Universidade Federal da Bahia (UFBA)instacron:UFBATEXTAfonso Fernandes da Silva. 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dc.title.pt_BR.fl_str_mv |
Contributions to phase transition of intermittent skew-product and piecewise monotone dynamics on the circle |
dc.title.alternative.pt_BR.fl_str_mv |
Contribuições para a transição de fase de skew-product intermitente e dinâmicas monótonas por partes no círculo |
title |
Contributions to phase transition of intermittent skew-product and piecewise monotone dynamics on the circle |
spellingShingle |
Contributions to phase transition of intermittent skew-product and piecewise monotone dynamics on the circle Silva, Afonso Fernandes da CNPQ::CIENCIAS EXATAS E DA TERRA CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA Phase transition Multifractal analysis Differential dynamical systems Ergodic theory Transição de fase Análise multifractal Sistemas dinâmicos diferenciais Teoria ergódica |
title_short |
Contributions to phase transition of intermittent skew-product and piecewise monotone dynamics on the circle |
title_full |
Contributions to phase transition of intermittent skew-product and piecewise monotone dynamics on the circle |
title_fullStr |
Contributions to phase transition of intermittent skew-product and piecewise monotone dynamics on the circle |
title_full_unstemmed |
Contributions to phase transition of intermittent skew-product and piecewise monotone dynamics on the circle |
title_sort |
Contributions to phase transition of intermittent skew-product and piecewise monotone dynamics on the circle |
author |
Silva, Afonso Fernandes da |
author_facet |
Silva, Afonso Fernandes da |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Nunes, Thiago Bomfim São Luiz |
dc.contributor.advisor1ID.fl_str_mv |
0000-0003-3120-2169 |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/8997137904643903 |
dc.contributor.referee1.fl_str_mv |
Nunes, Thiago Bomfim São Luiz |
dc.contributor.referee1ID.fl_str_mv |
0000-0003-3120-2169 |
dc.contributor.referee1Lattes.fl_str_mv |
http://lattes.cnpq.br/8997137904643903 |
dc.contributor.referee2.fl_str_mv |
Araujo, Vitor Domingos Martins de |
dc.contributor.referee2Lattes.fl_str_mv |
http://lattes.cnpq.br/4817632811350748 |
dc.contributor.referee3.fl_str_mv |
Varandas, Paulo Cesar Rodrigues Pinto |
dc.contributor.referee3ID.fl_str_mv |
0000-0002-0902-8718 |
dc.contributor.referee3Lattes.fl_str_mv |
http://lattes.cnpq.br/1450367699820349 |
dc.contributor.referee4.fl_str_mv |
Cruz, Anderson Reis da |
dc.contributor.referee4ID.fl_str_mv |
0000-0001-7928-4891 |
dc.contributor.referee4Lattes.fl_str_mv |
http://lattes.cnpq.br/8911485243130142 |
dc.contributor.referee5.fl_str_mv |
Bortolotti, Ricardo Turolla |
dc.contributor.referee5Lattes.fl_str_mv |
http://lattes.cnpq.br/5596171733972807 |
dc.contributor.authorLattes.fl_str_mv |
https://lattes.cnpq.br/0025628612607760 |
dc.contributor.author.fl_str_mv |
Silva, Afonso Fernandes da |
contributor_str_mv |
Nunes, Thiago Bomfim São Luiz Nunes, Thiago Bomfim São Luiz Araujo, Vitor Domingos Martins de Varandas, Paulo Cesar Rodrigues Pinto Cruz, Anderson Reis da Bortolotti, Ricardo Turolla |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
topic |
CNPQ::CIENCIAS EXATAS E DA TERRA CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA Phase transition Multifractal analysis Differential dynamical systems Ergodic theory Transição de fase Análise multifractal Sistemas dinâmicos diferenciais Teoria ergódica |
dc.subject.por.fl_str_mv |
Phase transition Multifractal analysis Differential dynamical systems Ergodic theory |
dc.subject.other.pt_BR.fl_str_mv |
Transição de fase Análise multifractal Sistemas dinâmicos diferenciais Teoria ergódica |
description |
It is known that any uniformly dusty or hyperbolic transitive dynamics do not it has phase transition with respect to the continuous Hölder potentials. When it comes to more general dynamics, it is still an open question to classify all the dynamics that They have transition with respect to a certain class of regular potentials. In dimension 1, according to Bomfim-Carneiro [BC21], every local C1+α-diffeomorphism in the transitive circle that is neither expander nor invertible has a single thermodynamic phase transition with respect to the geometric potential, in other words, the topological pressure function R ∋ t 7→ Ptop(f, −tlog |Df|) is analytic except at a point t0 ∈ (0, 1). They also proved spectral phase transition, i.e., the transfer operator Lf,−tlog |Df| Acting in the space of continuous Hölder functions, there is a spectral gap for all t < t0 and There is no spectral gap for T ≥ T0. Our goal is to prove similar results for two special classes of dynamics: partially codimensional 1 endomorphisms hyperbolic and monotonous dynamics by parts in the circle transitive. For high-dimensional endomorphisms, we proved that the thermodynamic and spectral phase transition results imply multifractal analysis for the Lyapunov spectrum. In particular We exhibit a class of partially hyperbolic endomorphisms that admit transition of thermodynamic and spectral phase with respect to the geometric potential in the central direction, and we describe multifractal analysis of the central Lyapunov exponents. For monotonous dynamics by parts in the circle, we prove that the set of continuous Hölder potentials that do not have thermodynamic and spectral phase transition is dense in the uniform topology and the set of continuous Hölder potentials that have phase transition is not dense in the uniform topology. We also get a transitional characterization in terms of the transfer operator and the convexity type of the topological pressure function. In In particular, we describe the behavior of the topological pressure function and the associated transfer. |
publishDate |
2023 |
dc.date.accessioned.fl_str_mv |
2023-11-20T12:16:20Z |
dc.date.available.fl_str_mv |
2023-11-20T12:16:20Z |
dc.date.issued.fl_str_mv |
2023-03-07 |
dc.type.driver.fl_str_mv |
Doutorado info:eu-repo/semantics/doctoralThesis |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
SILVA, Afonso Fernandes da. Contributions to phase transition of intermittent skew-product and piecewise monotone dynamics on the circle: a method for assessing quality attributes in self-adaptive systems. 2023. 79 f. Tese (Doutorado em Matemática) Instituto de Matemática e Estatística, Universidade Federal da Bahia, Salvador, Ba, 2023. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufba.br/handle/ri/38509 |
identifier_str_mv |
SILVA, Afonso Fernandes da. Contributions to phase transition of intermittent skew-product and piecewise monotone dynamics on the circle: a method for assessing quality attributes in self-adaptive systems. 2023. 79 f. Tese (Doutorado em Matemática) Instituto de Matemática e Estatística, Universidade Federal da Bahia, Salvador, Ba, 2023. |
url |
https://repositorio.ufba.br/handle/ri/38509 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal da Bahia |
dc.publisher.program.fl_str_mv |
Pós-Graduação em Matemática (PGMAT) |
dc.publisher.initials.fl_str_mv |
UFBA |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
Instituto de Matemática |
publisher.none.fl_str_mv |
Universidade Federal da Bahia |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFBA instname:Universidade Federal da Bahia (UFBA) instacron:UFBA |
instname_str |
Universidade Federal da Bahia (UFBA) |
instacron_str |
UFBA |
institution |
UFBA |
reponame_str |
Repositório Institucional da UFBA |
collection |
Repositório Institucional da UFBA |
bitstream.url.fl_str_mv |
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MD5 MD5 MD5 MD5 MD5 MD5 |
repository.name.fl_str_mv |
Repositório Institucional da UFBA - Universidade Federal da Bahia (UFBA) |
repository.mail.fl_str_mv |
|
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1808459905026228224 |