Phase Transitions for One-Dimensional Lorenz-Like Expanding Maps

Detalhes bibliográficos
Autor(a) principal: Gouveia, Márcio [UNESP]
Data de Publicação: 2022
Outros Autores: Oler, Juliano G.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1007/s00574-022-00310-y
http://hdl.handle.net/11449/240749
Resumo: Given an one-dimensional Lorenz-like expanding map we describe a class A of potentials ϕ: [0 , 1] ⟶ R admitting at most one equilibrium measure and we construct a family of continuous but not weak-Hölder continuous potentials for which we observe phase transitions. This give a certain generalization of the results proved in Pesin and Zhang (J Stat Phys 122(6):1095–1110, 2006), where the authors have proved this for a smaller class of potentials, that is, for uniformly expanding maps and weak-Hölder continuous potentials. Indeed, the class A form an open and dense subset of C([0 , 1] , R) , with the usual C topology.
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spelling Phase Transitions for One-Dimensional Lorenz-Like Expanding MapsEquilibrium measureLorenz mapsGiven an one-dimensional Lorenz-like expanding map we describe a class A of potentials ϕ: [0 , 1] ⟶ R admitting at most one equilibrium measure and we construct a family of continuous but not weak-Hölder continuous potentials for which we observe phase transitions. This give a certain generalization of the results proved in Pesin and Zhang (J Stat Phys 122(6):1095–1110, 2006), where the authors have proved this for a smaller class of potentials, that is, for uniformly expanding maps and weak-Hölder continuous potentials. Indeed, the class A form an open and dense subset of C([0 , 1] , R) , with the usual C topology.IBILCE-UNESP, São PauloFAMAT-UFU, Minas GeraisIBILCE-UNESP, São PauloUniversidade Estadual Paulista (UNESP)FAMAT-UFUGouveia, Márcio [UNESP]Oler, Juliano G.2023-03-01T20:31:15Z2023-03-01T20:31:15Z2022-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1007/s00574-022-00310-yBulletin of the Brazilian Mathematical Society.1678-7544http://hdl.handle.net/11449/24074910.1007/s00574-022-00310-y2-s2.0-85137070463Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengBulletin of the Brazilian Mathematical Societyinfo:eu-repo/semantics/openAccess2023-03-01T20:31:15Zoai:repositorio.unesp.br:11449/240749Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T23:12:18.859749Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Phase Transitions for One-Dimensional Lorenz-Like Expanding Maps
title Phase Transitions for One-Dimensional Lorenz-Like Expanding Maps
spellingShingle Phase Transitions for One-Dimensional Lorenz-Like Expanding Maps
Gouveia, Márcio [UNESP]
Equilibrium measure
Lorenz maps
title_short Phase Transitions for One-Dimensional Lorenz-Like Expanding Maps
title_full Phase Transitions for One-Dimensional Lorenz-Like Expanding Maps
title_fullStr Phase Transitions for One-Dimensional Lorenz-Like Expanding Maps
title_full_unstemmed Phase Transitions for One-Dimensional Lorenz-Like Expanding Maps
title_sort Phase Transitions for One-Dimensional Lorenz-Like Expanding Maps
author Gouveia, Márcio [UNESP]
author_facet Gouveia, Márcio [UNESP]
Oler, Juliano G.
author_role author
author2 Oler, Juliano G.
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
FAMAT-UFU
dc.contributor.author.fl_str_mv Gouveia, Márcio [UNESP]
Oler, Juliano G.
dc.subject.por.fl_str_mv Equilibrium measure
Lorenz maps
topic Equilibrium measure
Lorenz maps
description Given an one-dimensional Lorenz-like expanding map we describe a class A of potentials ϕ: [0 , 1] ⟶ R admitting at most one equilibrium measure and we construct a family of continuous but not weak-Hölder continuous potentials for which we observe phase transitions. This give a certain generalization of the results proved in Pesin and Zhang (J Stat Phys 122(6):1095–1110, 2006), where the authors have proved this for a smaller class of potentials, that is, for uniformly expanding maps and weak-Hölder continuous potentials. Indeed, the class A form an open and dense subset of C([0 , 1] , R) , with the usual C topology.
publishDate 2022
dc.date.none.fl_str_mv 2022-01-01
2023-03-01T20:31:15Z
2023-03-01T20:31:15Z
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/10.1007/s00574-022-00310-y
Bulletin of the Brazilian Mathematical Society.
1678-7544
http://hdl.handle.net/11449/240749
10.1007/s00574-022-00310-y
2-s2.0-85137070463
url http://dx.doi.org/10.1007/s00574-022-00310-y
http://hdl.handle.net/11449/240749
identifier_str_mv Bulletin of the Brazilian Mathematical Society.
1678-7544
10.1007/s00574-022-00310-y
2-s2.0-85137070463
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Bulletin of the Brazilian Mathematical Society
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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)
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