Global dynamics and diffusion in the rational standard map

Autores
Cincotta, Pablo Miguel; Simó, Carles
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we study the dynamics of the Rational Standard Map, which is a generalization of theStandard Map. It depends on two parameters, the usual K and a new one, 0 ≤ μ < 1, that breaksthe entire character of the perturbing function. By means of analytical and numerical methods it isshown that this system presents significant differences with respect to the classical Standard Map. Inparticular, for relatively large values of K the integer and semi-integer resonances are stable for somerange of μ values. Moreover, for K not small and near suitable values of μ , its dynamics could beassumed to be well represented by a nearly integrable system. On the other hand, periodic solutionsor accelerator modes also show differences between this map and the standard one. For instance,in case of K ≈ 2 π accelerator modes exist for μ less than some critical value but also within verynarrow intervals when 0 . 9 < μ < 1. Big differences for the domains of existence of rotationallyinvariant curves (much larger, for μ moderate, or much smaller, for μ close to 1 than for the standardmap) appear. While anomalies in the diffusion are observed, for large values of the parameters, thesystem becomes close to an ergodic one.
Fil: Cincotta, Pablo Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina
Fil: Simó, Carles. Universidad de Barcelona; España
Materia
AREE PRESERVING MAPS
RATIONAL STANDARD MAP
CHAOTIC DIFFUSION
SHANNON ENTROPY
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/142052

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spelling Global dynamics and diffusion in the rational standard mapCincotta, Pablo MiguelSimó, CarlesAREE PRESERVING MAPSRATIONAL STANDARD MAPCHAOTIC DIFFUSIONSHANNON ENTROPYhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1In this paper we study the dynamics of the Rational Standard Map, which is a generalization of theStandard Map. It depends on two parameters, the usual K and a new one, 0 ≤ μ < 1, that breaksthe entire character of the perturbing function. By means of analytical and numerical methods it isshown that this system presents significant differences with respect to the classical Standard Map. Inparticular, for relatively large values of K the integer and semi-integer resonances are stable for somerange of μ values. Moreover, for K not small and near suitable values of μ , its dynamics could beassumed to be well represented by a nearly integrable system. On the other hand, periodic solutionsor accelerator modes also show differences between this map and the standard one. For instance,in case of K ≈ 2 π accelerator modes exist for μ less than some critical value but also within verynarrow intervals when 0 . 9 < μ < 1. Big differences for the domains of existence of rotationallyinvariant curves (much larger, for μ moderate, or much smaller, for μ close to 1 than for the standardmap) appear. While anomalies in the diffusion are observed, for large values of the parameters, thesystem becomes close to an ergodic one.Fil: Cincotta, Pablo Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; ArgentinaFil: Simó, Carles. Universidad de Barcelona; EspañaElsevier Science2020-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/142052Cincotta, Pablo Miguel; Simó, Carles; Global dynamics and diffusion in the rational standard map; Elsevier Science; Physica D - Nonlinear Phenomena; 413; 12-2020; 132661, 1-140167-2789CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://linkinghub.elsevier.com/retrieve/pii/S0167278919308140info:eu-repo/semantics/altIdentifier/doi/10.1016/j.physd.2020.132661info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:46:52Zoai:ri.conicet.gov.ar:11336/142052instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:46:52.665CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Global dynamics and diffusion in the rational standard map
title Global dynamics and diffusion in the rational standard map
spellingShingle Global dynamics and diffusion in the rational standard map
Cincotta, Pablo Miguel
AREE PRESERVING MAPS
RATIONAL STANDARD MAP
CHAOTIC DIFFUSION
SHANNON ENTROPY
title_short Global dynamics and diffusion in the rational standard map
title_full Global dynamics and diffusion in the rational standard map
title_fullStr Global dynamics and diffusion in the rational standard map
title_full_unstemmed Global dynamics and diffusion in the rational standard map
title_sort Global dynamics and diffusion in the rational standard map
dc.creator.none.fl_str_mv Cincotta, Pablo Miguel
Simó, Carles
author Cincotta, Pablo Miguel
author_facet Cincotta, Pablo Miguel
Simó, Carles
author_role author
author2 Simó, Carles
author2_role author
dc.subject.none.fl_str_mv AREE PRESERVING MAPS
RATIONAL STANDARD MAP
CHAOTIC DIFFUSION
SHANNON ENTROPY
topic AREE PRESERVING MAPS
RATIONAL STANDARD MAP
CHAOTIC DIFFUSION
SHANNON ENTROPY
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we study the dynamics of the Rational Standard Map, which is a generalization of theStandard Map. It depends on two parameters, the usual K and a new one, 0 ≤ μ < 1, that breaksthe entire character of the perturbing function. By means of analytical and numerical methods it isshown that this system presents significant differences with respect to the classical Standard Map. Inparticular, for relatively large values of K the integer and semi-integer resonances are stable for somerange of μ values. Moreover, for K not small and near suitable values of μ , its dynamics could beassumed to be well represented by a nearly integrable system. On the other hand, periodic solutionsor accelerator modes also show differences between this map and the standard one. For instance,in case of K ≈ 2 π accelerator modes exist for μ less than some critical value but also within verynarrow intervals when 0 . 9 < μ < 1. Big differences for the domains of existence of rotationallyinvariant curves (much larger, for μ moderate, or much smaller, for μ close to 1 than for the standardmap) appear. While anomalies in the diffusion are observed, for large values of the parameters, thesystem becomes close to an ergodic one.
Fil: Cincotta, Pablo Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina
Fil: Simó, Carles. Universidad de Barcelona; España
description In this paper we study the dynamics of the Rational Standard Map, which is a generalization of theStandard Map. It depends on two parameters, the usual K and a new one, 0 ≤ μ < 1, that breaksthe entire character of the perturbing function. By means of analytical and numerical methods it isshown that this system presents significant differences with respect to the classical Standard Map. Inparticular, for relatively large values of K the integer and semi-integer resonances are stable for somerange of μ values. Moreover, for K not small and near suitable values of μ , its dynamics could beassumed to be well represented by a nearly integrable system. On the other hand, periodic solutionsor accelerator modes also show differences between this map and the standard one. For instance,in case of K ≈ 2 π accelerator modes exist for μ less than some critical value but also within verynarrow intervals when 0 . 9 < μ < 1. Big differences for the domains of existence of rotationallyinvariant curves (much larger, for μ moderate, or much smaller, for μ close to 1 than for the standardmap) appear. While anomalies in the diffusion are observed, for large values of the parameters, thesystem becomes close to an ergodic one.
publishDate 2020
dc.date.none.fl_str_mv 2020-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/142052
Cincotta, Pablo Miguel; Simó, Carles; Global dynamics and diffusion in the rational standard map; Elsevier Science; Physica D - Nonlinear Phenomena; 413; 12-2020; 132661, 1-14
0167-2789
CONICET Digital
CONICET
url http://hdl.handle.net/11336/142052
identifier_str_mv Cincotta, Pablo Miguel; Simó, Carles; Global dynamics and diffusion in the rational standard map; Elsevier Science; Physica D - Nonlinear Phenomena; 413; 12-2020; 132661, 1-14
0167-2789
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://linkinghub.elsevier.com/retrieve/pii/S0167278919308140
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.physd.2020.132661
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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