Finding critical exponents for two-dimensional Hamiltonian maps

Detalhes bibliográficos
Autor(a) principal: De Oliveira, Juliano A. [UNESP]
Data de Publicação: 2010
Outros Autores: Bizão, R. A. [UNESP], Leonel, Edson D. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1103/PhysRevE.81.046212
http://hdl.handle.net/11449/225841
Resumo: The transition from integrability to nonintegrability for a set of two-dimensional Hamiltonian mappings exhibiting mixed phase space is considered. The phase space of such mappings show a large chaotic sea surrounding Kolmogorov-Arnold-Moser islands and limited by a set of invariant tori. The description of the phase transition is made by the use of scaling functions for average quantities of the mapping averaged along the chaotic sea. The critical exponents are obtained via extensive numerical simulations. Given the mappings considered are parametrized by an exponent γ in one of the dynamical variables, the critical exponents that characterize the scaling functions are obtained for many different values of γ. Therefore classes of universality are defined. © 2010 The American Physical Society.
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spelling Finding critical exponents for two-dimensional Hamiltonian mapsThe transition from integrability to nonintegrability for a set of two-dimensional Hamiltonian mappings exhibiting mixed phase space is considered. The phase space of such mappings show a large chaotic sea surrounding Kolmogorov-Arnold-Moser islands and limited by a set of invariant tori. The description of the phase transition is made by the use of scaling functions for average quantities of the mapping averaged along the chaotic sea. The critical exponents are obtained via extensive numerical simulations. Given the mappings considered are parametrized by an exponent γ in one of the dynamical variables, the critical exponents that characterize the scaling functions are obtained for many different values of γ. Therefore classes of universality are defined. © 2010 The American Physical Society.Departamento de Estatística Matemática Aplicada e Computação Universidade Estadual Paulista, 1515 Bela Vista, CEP 13506-700 Rio Claro, SPDepartamento de Estatística Matemática Aplicada e Computação Universidade Estadual Paulista, 1515 Bela Vista, CEP 13506-700 Rio Claro, SPUniversidade Estadual Paulista (UNESP)De Oliveira, Juliano A. [UNESP]Bizão, R. A. [UNESP]Leonel, Edson D. [UNESP]2022-04-28T21:01:17Z2022-04-28T21:01:17Z2010-04-26info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1103/PhysRevE.81.046212Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, v. 81, n. 4, 2010.1539-37551550-2376http://hdl.handle.net/11449/22584110.1103/PhysRevE.81.0462122-s2.0-77951710220Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPhysical Review E - Statistical, Nonlinear, and Soft Matter Physicsinfo:eu-repo/semantics/openAccess2022-04-28T21:01:17Zoai:repositorio.unesp.br:11449/225841Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T15:10:04.925351Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Finding critical exponents for two-dimensional Hamiltonian maps
title Finding critical exponents for two-dimensional Hamiltonian maps
spellingShingle Finding critical exponents for two-dimensional Hamiltonian maps
De Oliveira, Juliano A. [UNESP]
title_short Finding critical exponents for two-dimensional Hamiltonian maps
title_full Finding critical exponents for two-dimensional Hamiltonian maps
title_fullStr Finding critical exponents for two-dimensional Hamiltonian maps
title_full_unstemmed Finding critical exponents for two-dimensional Hamiltonian maps
title_sort Finding critical exponents for two-dimensional Hamiltonian maps
author De Oliveira, Juliano A. [UNESP]
author_facet De Oliveira, Juliano A. [UNESP]
Bizão, R. A. [UNESP]
Leonel, Edson D. [UNESP]
author_role author
author2 Bizão, R. A. [UNESP]
Leonel, Edson D. [UNESP]
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv De Oliveira, Juliano A. [UNESP]
Bizão, R. A. [UNESP]
Leonel, Edson D. [UNESP]
description The transition from integrability to nonintegrability for a set of two-dimensional Hamiltonian mappings exhibiting mixed phase space is considered. The phase space of such mappings show a large chaotic sea surrounding Kolmogorov-Arnold-Moser islands and limited by a set of invariant tori. The description of the phase transition is made by the use of scaling functions for average quantities of the mapping averaged along the chaotic sea. The critical exponents are obtained via extensive numerical simulations. Given the mappings considered are parametrized by an exponent γ in one of the dynamical variables, the critical exponents that characterize the scaling functions are obtained for many different values of γ. Therefore classes of universality are defined. © 2010 The American Physical Society.
publishDate 2010
dc.date.none.fl_str_mv 2010-04-26
2022-04-28T21:01:17Z
2022-04-28T21:01:17Z
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/10.1103/PhysRevE.81.046212
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, v. 81, n. 4, 2010.
1539-3755
1550-2376
http://hdl.handle.net/11449/225841
10.1103/PhysRevE.81.046212
2-s2.0-77951710220
url http://dx.doi.org/10.1103/PhysRevE.81.046212
http://hdl.handle.net/11449/225841
identifier_str_mv Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, v. 81, n. 4, 2010.
1539-3755
1550-2376
10.1103/PhysRevE.81.046212
2-s2.0-77951710220
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
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
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