Thermodynamic formalism for general IFS and quantum channels

Detalhes bibliográficos
Autor(a) principal: Brasil, Jader Eckert
Data de Publicação: 2022
Tipo de documento: Tese
Idioma: eng
Título da fonte: Biblioteca Digital de Teses e Dissertações da UFRGS
Texto Completo: http://hdl.handle.net/10183/247521
Resumo: This chapter is part of [BOS22] and introduces a theory of Thermodynamic Formalism for Iterated Function Systems with Measures (IFSm). We study the spectral properties of the Transfer and Markov operators associated to a IFSm. We introduce variational formulations for the topological entropy of holonomic measures and the topological pressure of IFSm given by a potential. A definition of equilibrium state is then natural and we prove its existence for any continuous potential. We show, in this setting, a uniqueness result for the equilibrium state requiring only the Gâteaux differentiability of the pressure functional.
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spelling Brasil, Jader EckertSouza, Rafael RigãoLopes, Artur Oscar2022-08-20T04:55:08Z2022http://hdl.handle.net/10183/247521001147086This chapter is part of [BOS22] and introduces a theory of Thermodynamic Formalism for Iterated Function Systems with Measures (IFSm). We study the spectral properties of the Transfer and Markov operators associated to a IFSm. We introduce variational formulations for the topological entropy of holonomic measures and the topological pressure of IFSm given by a potential. A definition of equilibrium state is then natural and we prove its existence for any continuous potential. We show, in this setting, a uniqueness result for the equilibrium state requiring only the Gâteaux differentiability of the pressure functional.application/pdfengFormalismo termodinamicoEntropiaAutovaloresOperadoresThermodynamic formalism for general IFS and quantum channelsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisUniversidade Federal do Rio Grande do SulInstituto de Matemática e EstatísticaPrograma de Pós-Graduação em MatemáticaPorto Alegre, BR-RS2022doutoradoinfo:eu-repo/semantics/openAccessreponame:Biblioteca Digital de Teses e Dissertações da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSTEXT001147086.pdf.txt001147086.pdf.txtExtracted Texttext/plain142180http://www.lume.ufrgs.br/bitstream/10183/247521/2/001147086.pdf.txt32fb34f685b3a25c0ee29dc20cf57ed9MD52ORIGINAL001147086.pdfTexto completo (inglês)application/pdf576219http://www.lume.ufrgs.br/bitstream/10183/247521/1/001147086.pdf999163568a772fe0dfc65251f8460848MD5110183/2475212022-08-21 04:38:52.431156oai:www.lume.ufrgs.br:10183/247521Biblioteca Digital de Teses e Dissertaçõeshttps://lume.ufrgs.br/handle/10183/2PUBhttps://lume.ufrgs.br/oai/requestlume@ufrgs.br||lume@ufrgs.bropendoar:18532022-08-21T07:38:52Biblioteca Digital de Teses e Dissertações da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false
dc.title.pt_BR.fl_str_mv Thermodynamic formalism for general IFS and quantum channels
title Thermodynamic formalism for general IFS and quantum channels
spellingShingle Thermodynamic formalism for general IFS and quantum channels
Brasil, Jader Eckert
Formalismo termodinamico
Entropia
Autovalores
Operadores
title_short Thermodynamic formalism for general IFS and quantum channels
title_full Thermodynamic formalism for general IFS and quantum channels
title_fullStr Thermodynamic formalism for general IFS and quantum channels
title_full_unstemmed Thermodynamic formalism for general IFS and quantum channels
title_sort Thermodynamic formalism for general IFS and quantum channels
author Brasil, Jader Eckert
author_facet Brasil, Jader Eckert
author_role author
dc.contributor.author.fl_str_mv Brasil, Jader Eckert
dc.contributor.advisor1.fl_str_mv Souza, Rafael Rigão
dc.contributor.advisor-co1.fl_str_mv Lopes, Artur Oscar
contributor_str_mv Souza, Rafael Rigão
Lopes, Artur Oscar
dc.subject.por.fl_str_mv Formalismo termodinamico
Entropia
Autovalores
Operadores
topic Formalismo termodinamico
Entropia
Autovalores
Operadores
description This chapter is part of [BOS22] and introduces a theory of Thermodynamic Formalism for Iterated Function Systems with Measures (IFSm). We study the spectral properties of the Transfer and Markov operators associated to a IFSm. We introduce variational formulations for the topological entropy of holonomic measures and the topological pressure of IFSm given by a potential. A definition of equilibrium state is then natural and we prove its existence for any continuous potential. We show, in this setting, a uniqueness result for the equilibrium state requiring only the Gâteaux differentiability of the pressure functional.
publishDate 2022
dc.date.accessioned.fl_str_mv 2022-08-20T04:55:08Z
dc.date.issued.fl_str_mv 2022
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/doctoralThesis
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dc.identifier.uri.fl_str_mv http://hdl.handle.net/10183/247521
dc.identifier.nrb.pt_BR.fl_str_mv 001147086
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dc.language.iso.fl_str_mv eng
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