A mechanism explaining the metamorphoses of KAM islands in nonhyperbolic chaotic scattering

Acknowledgements The work of A. R. N., J. M. S., and M. A. F. S. has been financially supported by the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERDF) under Project No. PID2019-105554GB-I00. The work of R. B. has been supported by the Spanish State Research Agen...

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Detalles Bibliográficos
Autores: Nieto, Alexandre R., Seoane, Jesús M., Barrio, Roberto, Sanjuán, Miguel A. F.
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad Rey Juan Carlos
Repositorio:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
OAI Identifier:oai:burjcdigital.urjc.es:10115/24384
Acceso en línea:https://hdl.handle.net/10115/24384
Access Level:acceso abierto
Palabra clave:Bifurcations
KAM tori
Periodic orbits
Numerical simulations
Hamiltonian systems
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spelling A mechanism explaining the metamorphoses of KAM islands in nonhyperbolic chaotic scatteringNieto, Alexandre R.Seoane, Jesús M.Barrio, RobertoSanjuán, Miguel A. F.BifurcationsKAM toriPeriodic orbitsNumerical simulationsHamiltonian systemsAcknowledgements The work of A. R. N., J. M. S., and M. A. F. S. has been financially supported by the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERDF) under Project No. PID2019-105554GB-I00. The work of R. B. has been supported by the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERDF) under Projects No. PGC2018-096026-B-I00 and PID2021-122961NB-I00, and European Regional Development Fund and Diputación General de Aragón under Projects No. E24-17R and LMP124-18. Funding Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.Abstract In the context of nonhyperbolic chaotic scattering, it has been shown that the evolution of the KAM islands exhibits four abrupt metamorphoses that strongly affect the predictability of Hamiltonian systems. It has been suggested that these metamorphoses are related to significant changes in the structure of the KAM islands. However, previous research has not provided an explanation of the mechanisms underlying the metamorphoses. Here, we show that they occur due to the formation of a homoclinic or heteroclinic tangle that breaks the internal structure of the main KAM island. We obtain similar qualitative results in a two-dimensional Hamiltonian system and a twodimensional area-preserving map. The equivalence of the results obtained in both systems suggests that the same four metamorphoses play an important role in conservative systems.Springer202320232022info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10115/24384reponame: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:10115/243842026-06-24T12:48:17Z
dc.title.none.fl_str_mv A mechanism explaining the metamorphoses of KAM islands in nonhyperbolic chaotic scattering
title A mechanism explaining the metamorphoses of KAM islands in nonhyperbolic chaotic scattering
spellingShingle A mechanism explaining the metamorphoses of KAM islands in nonhyperbolic chaotic scattering
Nieto, Alexandre R.
Bifurcations
KAM tori
Periodic orbits
Numerical simulations
Hamiltonian systems
title_short A mechanism explaining the metamorphoses of KAM islands in nonhyperbolic chaotic scattering
title_full A mechanism explaining the metamorphoses of KAM islands in nonhyperbolic chaotic scattering
title_fullStr A mechanism explaining the metamorphoses of KAM islands in nonhyperbolic chaotic scattering
title_full_unstemmed A mechanism explaining the metamorphoses of KAM islands in nonhyperbolic chaotic scattering
title_sort A mechanism explaining the metamorphoses of KAM islands in nonhyperbolic chaotic scattering
dc.creator.none.fl_str_mv Nieto, Alexandre R.
Seoane, Jesús M.
Barrio, Roberto
Sanjuán, Miguel A. F.
author Nieto, Alexandre R.
author_facet Nieto, Alexandre R.
Seoane, Jesús M.
Barrio, Roberto
Sanjuán, Miguel A. F.
author_role author
author2 Seoane, Jesús M.
Barrio, Roberto
Sanjuán, Miguel A. F.
author2_role author
author
author
dc.subject.none.fl_str_mv Bifurcations
KAM tori
Periodic orbits
Numerical simulations
Hamiltonian systems
topic Bifurcations
KAM tori
Periodic orbits
Numerical simulations
Hamiltonian systems
description Acknowledgements The work of A. R. N., J. M. S., and M. A. F. S. has been financially supported by the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERDF) under Project No. PID2019-105554GB-I00. The work of R. B. has been supported by the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERDF) under Projects No. PGC2018-096026-B-I00 and PID2021-122961NB-I00, and European Regional Development Fund and Diputación General de Aragón under Projects No. E24-17R and LMP124-18. Funding Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.
publishDate 2022
dc.date.none.fl_str_mv 2022
2023
2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10115/24384
url https://hdl.handle.net/10115/24384
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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