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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/142052
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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 |
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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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13.13397 |