Phase Transitions for One-Dimensional Lorenz-Like Expanding Maps
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | |
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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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) |
repository.mail.fl_str_mv |
|
_version_ |
1808129499347288064 |