Numerical and Theoretical Studies on the Rational Standard Map at Moderate-to-Large Values of the Amplitude Parameter
- Autores
- Cincotta, Pablo Miguel; Giordano, Claudia Marcela; Simó, Carles
- Año de publicación
- 2023
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In this work an exhaustive numerical and analytical investigation of the dynamicsof a bi-parametric symplectic map, the so-called rational standard map, at moderate-to-largevalues of the amplitude parameter is addressed. After reviewing the model, a discussionconcerning an analytical determination of the maximum Lyapunov exponent is providedtogether with thorough numerical experiments. The theoretical results are obtained in thelimit of a nearly uniform distribution of the phase values. Correlations among phases lead todepartures from the expected estimates. In this direction, a detailed study of the role of stableperiodic islands of periods 1, 2 and 4 is included. Finally, an experimental relationship betweenthe Lyapunov and instability times is shown, while an analytical one applies when correlationsare irrelevant, which is the case, in general, for large values of the amplitude parameter.
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: Giordano, Claudia Marcela. 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. Instituto de Matematica ; Facultad de Matematicas ; Universidad de Barcelona; - Materia
-
ANALYTICAL AND NUMERICAL METGODS
PERIODIC ORBITS
CHAOS
AREA-PRESERVING MAPS - 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:11336/235519
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Numerical and Theoretical Studies on the Rational Standard Map at Moderate-to-Large Values of the Amplitude ParameterCincotta, Pablo MiguelGiordano, Claudia MarcelaSimó, CarlesANALYTICAL AND NUMERICAL METGODSPERIODIC ORBITSCHAOSAREA-PRESERVING MAPShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1In this work an exhaustive numerical and analytical investigation of the dynamicsof a bi-parametric symplectic map, the so-called rational standard map, at moderate-to-largevalues of the amplitude parameter is addressed. After reviewing the model, a discussionconcerning an analytical determination of the maximum Lyapunov exponent is providedtogether with thorough numerical experiments. The theoretical results are obtained in thelimit of a nearly uniform distribution of the phase values. Correlations among phases lead todepartures from the expected estimates. In this direction, a detailed study of the role of stableperiodic islands of periods 1, 2 and 4 is included. Finally, an experimental relationship betweenthe Lyapunov and instability times is shown, while an analytical one applies when correlationsare irrelevant, which is the case, in general, for large values of the amplitude parameter.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: Giordano, Claudia Marcela. 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. Instituto de Matematica ; Facultad de Matematicas ; Universidad de Barcelona;Springer2023-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/235519Cincotta, Pablo Miguel; Giordano, Claudia Marcela; Simó, Carles; Numerical and Theoretical Studies on the Rational Standard Map at Moderate-to-Large Values of the Amplitude Parameter; Springer; Regular And Chaotic Dynamics; 28; 3; 6-2023; 265-2941560-35471468-4845CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://rcd.ics.org.ru/archive/volume-28-number-3/info:eu-repo/semantics/altIdentifier/doi/10.1134/S1560354723030024info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:10:06Zoai:ri.conicet.gov.ar:11336/235519instacron: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 10:10:06.902CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Numerical and Theoretical Studies on the Rational Standard Map at Moderate-to-Large Values of the Amplitude Parameter |
title |
Numerical and Theoretical Studies on the Rational Standard Map at Moderate-to-Large Values of the Amplitude Parameter |
spellingShingle |
Numerical and Theoretical Studies on the Rational Standard Map at Moderate-to-Large Values of the Amplitude Parameter Cincotta, Pablo Miguel ANALYTICAL AND NUMERICAL METGODS PERIODIC ORBITS CHAOS AREA-PRESERVING MAPS |
title_short |
Numerical and Theoretical Studies on the Rational Standard Map at Moderate-to-Large Values of the Amplitude Parameter |
title_full |
Numerical and Theoretical Studies on the Rational Standard Map at Moderate-to-Large Values of the Amplitude Parameter |
title_fullStr |
Numerical and Theoretical Studies on the Rational Standard Map at Moderate-to-Large Values of the Amplitude Parameter |
title_full_unstemmed |
Numerical and Theoretical Studies on the Rational Standard Map at Moderate-to-Large Values of the Amplitude Parameter |
title_sort |
Numerical and Theoretical Studies on the Rational Standard Map at Moderate-to-Large Values of the Amplitude Parameter |
dc.creator.none.fl_str_mv |
Cincotta, Pablo Miguel Giordano, Claudia Marcela Simó, Carles |
author |
Cincotta, Pablo Miguel |
author_facet |
Cincotta, Pablo Miguel Giordano, Claudia Marcela Simó, Carles |
author_role |
author |
author2 |
Giordano, Claudia Marcela Simó, Carles |
author2_role |
author author |
dc.subject.none.fl_str_mv |
ANALYTICAL AND NUMERICAL METGODS PERIODIC ORBITS CHAOS AREA-PRESERVING MAPS |
topic |
ANALYTICAL AND NUMERICAL METGODS PERIODIC ORBITS CHAOS AREA-PRESERVING MAPS |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 https://purl.org/becyt/ford/1.3 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
In this work an exhaustive numerical and analytical investigation of the dynamicsof a bi-parametric symplectic map, the so-called rational standard map, at moderate-to-largevalues of the amplitude parameter is addressed. After reviewing the model, a discussionconcerning an analytical determination of the maximum Lyapunov exponent is providedtogether with thorough numerical experiments. The theoretical results are obtained in thelimit of a nearly uniform distribution of the phase values. Correlations among phases lead todepartures from the expected estimates. In this direction, a detailed study of the role of stableperiodic islands of periods 1, 2 and 4 is included. Finally, an experimental relationship betweenthe Lyapunov and instability times is shown, while an analytical one applies when correlationsare irrelevant, which is the case, in general, for large values of the amplitude parameter. 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: Giordano, Claudia Marcela. 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. Instituto de Matematica ; Facultad de Matematicas ; Universidad de Barcelona; |
description |
In this work an exhaustive numerical and analytical investigation of the dynamicsof a bi-parametric symplectic map, the so-called rational standard map, at moderate-to-largevalues of the amplitude parameter is addressed. After reviewing the model, a discussionconcerning an analytical determination of the maximum Lyapunov exponent is providedtogether with thorough numerical experiments. The theoretical results are obtained in thelimit of a nearly uniform distribution of the phase values. Correlations among phases lead todepartures from the expected estimates. In this direction, a detailed study of the role of stableperiodic islands of periods 1, 2 and 4 is included. Finally, an experimental relationship betweenthe Lyapunov and instability times is shown, while an analytical one applies when correlationsare irrelevant, which is the case, in general, for large values of the amplitude parameter. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-06 |
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/11336/235519 Cincotta, Pablo Miguel; Giordano, Claudia Marcela; Simó, Carles; Numerical and Theoretical Studies on the Rational Standard Map at Moderate-to-Large Values of the Amplitude Parameter; Springer; Regular And Chaotic Dynamics; 28; 3; 6-2023; 265-294 1560-3547 1468-4845 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/235519 |
identifier_str_mv |
Cincotta, Pablo Miguel; Giordano, Claudia Marcela; Simó, Carles; Numerical and Theoretical Studies on the Rational Standard Map at Moderate-to-Large Values of the Amplitude Parameter; Springer; Regular And Chaotic Dynamics; 28; 3; 6-2023; 265-294 1560-3547 1468-4845 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/http://rcd.ics.org.ru/archive/volume-28-number-3/ info:eu-repo/semantics/altIdentifier/doi/10.1134/S1560354723030024 |
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 application/pdf |
dc.publisher.none.fl_str_mv |
Springer |
publisher.none.fl_str_mv |
Springer |
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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1842270106795638784 |
score |
13.13397 |