Diffusion entropy analysis in billiard systems
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1103/PhysRevE.100.042207 http://hdl.handle.net/11449/198084 |
Resumo: | In this work we investigate how the behavior of the Shannon entropy can be used to measure the diffusion exponent of a set of initial conditions in two systems: (i) standard map and (ii) the oval billiard. We are interested in the diffusion near the main island in the phase space, where stickiness is observed. We calculate the diffusion exponent for many values of the nonlinear parameter of the standard map where the size and shape of the main island change as the parameter varies. We show that the changes of behavior in the diffusion exponent are related with the changes in the area of the main island and show that when the area of the main island is abruptly reduced, due to the destruction of invariant tori and, consequently, creation of hyperbolic and elliptic fixed points, the diffusion exponent grows. |
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Diffusion entropy analysis in billiard systemsIn this work we investigate how the behavior of the Shannon entropy can be used to measure the diffusion exponent of a set of initial conditions in two systems: (i) standard map and (ii) the oval billiard. We are interested in the diffusion near the main island in the phase space, where stickiness is observed. We calculate the diffusion exponent for many values of the nonlinear parameter of the standard map where the size and shape of the main island change as the parameter varies. We show that the changes of behavior in the diffusion exponent are related with the changes in the area of the main island and show that when the area of the main island is abruptly reduced, due to the destruction of invariant tori and, consequently, creation of hyperbolic and elliptic fixed points, the diffusion exponent grows.Instituto de Física IFUSP-Universidade de São Paulo Cidade Universitária, Rua do MatãoDepartamento de Física UNESP-Universidade Estadual Paulista Bela VistaDepartamento de Física UNESP-Universidade Estadual Paulista Bela VistaUniversidade de São Paulo (USP)Universidade Estadual Paulista (Unesp)Díaz, Gabriel I.Palmero, Matheus S.Caldas, Iberê LuizLeonel, Edson D. [UNESP]2020-12-12T00:58:47Z2020-12-12T00:58:47Z2019-10-07info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1103/PhysRevE.100.042207Physical Review E, v. 100, n. 4, 2019.2470-00532470-0045http://hdl.handle.net/11449/19808410.1103/PhysRevE.100.0422072-s2.0-85074455263Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPhysical Review Einfo:eu-repo/semantics/openAccess2021-10-23T08:32:08Zoai:repositorio.unesp.br:11449/198084Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T13:46:13.745101Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Diffusion entropy analysis in billiard systems |
title |
Diffusion entropy analysis in billiard systems |
spellingShingle |
Diffusion entropy analysis in billiard systems Díaz, Gabriel I. |
title_short |
Diffusion entropy analysis in billiard systems |
title_full |
Diffusion entropy analysis in billiard systems |
title_fullStr |
Diffusion entropy analysis in billiard systems |
title_full_unstemmed |
Diffusion entropy analysis in billiard systems |
title_sort |
Diffusion entropy analysis in billiard systems |
author |
Díaz, Gabriel I. |
author_facet |
Díaz, Gabriel I. Palmero, Matheus S. Caldas, Iberê Luiz Leonel, Edson D. [UNESP] |
author_role |
author |
author2 |
Palmero, Matheus S. Caldas, Iberê Luiz Leonel, Edson D. [UNESP] |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Universidade de São Paulo (USP) Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Díaz, Gabriel I. Palmero, Matheus S. Caldas, Iberê Luiz Leonel, Edson D. [UNESP] |
description |
In this work we investigate how the behavior of the Shannon entropy can be used to measure the diffusion exponent of a set of initial conditions in two systems: (i) standard map and (ii) the oval billiard. We are interested in the diffusion near the main island in the phase space, where stickiness is observed. We calculate the diffusion exponent for many values of the nonlinear parameter of the standard map where the size and shape of the main island change as the parameter varies. We show that the changes of behavior in the diffusion exponent are related with the changes in the area of the main island and show that when the area of the main island is abruptly reduced, due to the destruction of invariant tori and, consequently, creation of hyperbolic and elliptic fixed points, the diffusion exponent grows. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-10-07 2020-12-12T00:58:47Z 2020-12-12T00:58:47Z |
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.100.042207 Physical Review E, v. 100, n. 4, 2019. 2470-0053 2470-0045 http://hdl.handle.net/11449/198084 10.1103/PhysRevE.100.042207 2-s2.0-85074455263 |
url |
http://dx.doi.org/10.1103/PhysRevE.100.042207 http://hdl.handle.net/11449/198084 |
identifier_str_mv |
Physical Review E, v. 100, n. 4, 2019. 2470-0053 2470-0045 10.1103/PhysRevE.100.042207 2-s2.0-85074455263 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Physical Review E |
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_ |
1808128274313773056 |