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
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/235519

id CONICETDig_d6a6aaefb5fc33ca2ed7592de540a095
oai_identifier_str oai:ri.conicet.gov.ar:11336/235519
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling 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
_version_ 1842270106795638784
score 13.13397