Systematic search for islets of stability in the standard map for large parameter values

Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature

Detalhes bibliográficos
Autores: Nieto, Alexandre R., Capeáns, Rubén, Sanjuan, Miguel A.F.
Formato: artículo
Fecha de publicación:2024
País:España
Recursos:Universidad Rey Juan Carlos
Repositorio:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
OAI Identifier:oai:burjcdigital.urjc.es:10115/35154
Acesso em linha:https://hdl.handle.net/10115/35154
Access Level:acceso abierto
Palavra-chave:Hamiltonian systems
Area-preserving maps
KAM tori
Numerical simulations
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spelling Systematic search for islets of stability in the standard map for large parameter valuesNieto, Alexandre R.Capeáns, RubénSanjuan, Miguel A.F.Hamiltonian systemsArea-preserving mapsKAM toriNumerical simulationsOpen Access funding provided thanks to the CRUE-CSIC agreement with Springer NatureIn the seminal paper, Chirikov (Phys Rep 52:263–379, 1979) showed that the standard map does not exhibit a boundary to chaos, but rather that there are small islands (“islets”) of stability for arbitrarily large values of the nonlinear perturbation. In this context, he established that the area of the islets in the phase space and the range of parameter values where they exist should decay following power laws with exponents and , respectively. In this paper, we carry out a systematic numerical search for islets of stability and we show that the power laws predicted by Chirikov hold. Furthermore, we use high-resolution 3D islets to reveal that the islets’ volume decays following a similar power law with exponent -3Springer202420242024info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10115/35154reponame:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlosinstname:Universidad Rey Juan CarlosInglésAtribución 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:burjcdigital.urjc.es:10115/351542026-06-24T12:48:17Z
dc.title.none.fl_str_mv Systematic search for islets of stability in the standard map for large parameter values
title Systematic search for islets of stability in the standard map for large parameter values
spellingShingle Systematic search for islets of stability in the standard map for large parameter values
Nieto, Alexandre R.
Hamiltonian systems
Area-preserving maps
KAM tori
Numerical simulations
title_short Systematic search for islets of stability in the standard map for large parameter values
title_full Systematic search for islets of stability in the standard map for large parameter values
title_fullStr Systematic search for islets of stability in the standard map for large parameter values
title_full_unstemmed Systematic search for islets of stability in the standard map for large parameter values
title_sort Systematic search for islets of stability in the standard map for large parameter values
dc.creator.none.fl_str_mv Nieto, Alexandre R.
Capeáns, Rubén
Sanjuan, Miguel A.F.
author Nieto, Alexandre R.
author_facet Nieto, Alexandre R.
Capeáns, Rubén
Sanjuan, Miguel A.F.
author_role author
author2 Capeáns, Rubén
Sanjuan, Miguel A.F.
author2_role author
author
dc.subject.none.fl_str_mv Hamiltonian systems
Area-preserving maps
KAM tori
Numerical simulations
topic Hamiltonian systems
Area-preserving maps
KAM tori
Numerical simulations
description Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature
publishDate 2024
dc.date.none.fl_str_mv 2024
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10115/35154
url https://hdl.handle.net/10115/35154
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv Atribución 4.0 Internacional
http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución 4.0 Internacional
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
instname:Universidad Rey Juan Carlos
instname_str Universidad Rey Juan Carlos
reponame_str BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
collection BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,81155

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