Testing the accuracy of the overlap criterion

Autores
Mestre, Martín Federico; Cincotta, Pablo Miguel; Giordano, Claudia Marcela
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Here we investigate the accuracy of the overlap criterion when applied to a simple near-integrable model in both its 2D and 3D versions. To this end, we consider, respectively, two and three quartic oscillators as the unperturbed system, and couple the degrees of freedom by a cubic, non-integrable perturbation. For both systems we compute the unperturbed resonances up to order O (e2), and model each resonance by means of the pendulum approximation in order to estimate the theoretical critical value of the perturbation parameter for a global transition to chaos. We perform several surface of sections for the bi-dimensional case to derive an empirical value to be compared to our theoretical estimation. Although both values are of the same order of magnitude, there is a significant difference between them. For the 3D case a numerical estimate is attained that we observe matches quite well the critical value resulting from theoretical means. This confirms once again that calculating resonances up to O (e2) suffices in order the overlap criterion to work out.
Facultad de Ciencias Astronómicas y Geofísicas
Materia
Astronomía
Chaos
Resonances
Theoretical and numerical method
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/130649

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network_name_str SEDICI (UNLP)
spelling Testing the accuracy of the overlap criterionMestre, Martín FedericoCincotta, Pablo MiguelGiordano, Claudia MarcelaAstronomíaChaosResonancesTheoretical and numerical methodHere we investigate the accuracy of the overlap criterion when applied to a simple near-integrable model in both its 2D and 3D versions. To this end, we consider, respectively, two and three quartic oscillators as the unperturbed system, and couple the degrees of freedom by a cubic, non-integrable perturbation. For both systems we compute the unperturbed resonances up to order O (e2), and model each resonance by means of the pendulum approximation in order to estimate the theoretical critical value of the perturbation parameter for a global transition to chaos. We perform several surface of sections for the bi-dimensional case to derive an empirical value to be compared to our theoretical estimation. Although both values are of the same order of magnitude, there is a significant difference between them. For the 3D case a numerical estimate is attained that we observe matches quite well the critical value resulting from theoretical means. This confirms once again that calculating resonances up to O (e2) suffices in order the overlap criterion to work out.Facultad de Ciencias Astronómicas y Geofísicas2009info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf180-189http://sedici.unlp.edu.ar/handle/10915/130649enginfo:eu-repo/semantics/altIdentifier/issn/0020-7462info:eu-repo/semantics/altIdentifier/arxiv/0807.2632info:eu-repo/semantics/altIdentifier/doi/10.1016/j.ijnonlinmec.2008.11.003info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International (CC BY 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:31:18Zoai:sedici.unlp.edu.ar:10915/130649Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:31:18.572SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Testing the accuracy of the overlap criterion
title Testing the accuracy of the overlap criterion
spellingShingle Testing the accuracy of the overlap criterion
Mestre, Martín Federico
Astronomía
Chaos
Resonances
Theoretical and numerical method
title_short Testing the accuracy of the overlap criterion
title_full Testing the accuracy of the overlap criterion
title_fullStr Testing the accuracy of the overlap criterion
title_full_unstemmed Testing the accuracy of the overlap criterion
title_sort Testing the accuracy of the overlap criterion
dc.creator.none.fl_str_mv Mestre, Martín Federico
Cincotta, Pablo Miguel
Giordano, Claudia Marcela
author Mestre, Martín Federico
author_facet Mestre, Martín Federico
Cincotta, Pablo Miguel
Giordano, Claudia Marcela
author_role author
author2 Cincotta, Pablo Miguel
Giordano, Claudia Marcela
author2_role author
author
dc.subject.none.fl_str_mv Astronomía
Chaos
Resonances
Theoretical and numerical method
topic Astronomía
Chaos
Resonances
Theoretical and numerical method
dc.description.none.fl_txt_mv Here we investigate the accuracy of the overlap criterion when applied to a simple near-integrable model in both its 2D and 3D versions. To this end, we consider, respectively, two and three quartic oscillators as the unperturbed system, and couple the degrees of freedom by a cubic, non-integrable perturbation. For both systems we compute the unperturbed resonances up to order O (e2), and model each resonance by means of the pendulum approximation in order to estimate the theoretical critical value of the perturbation parameter for a global transition to chaos. We perform several surface of sections for the bi-dimensional case to derive an empirical value to be compared to our theoretical estimation. Although both values are of the same order of magnitude, there is a significant difference between them. For the 3D case a numerical estimate is attained that we observe matches quite well the critical value resulting from theoretical means. This confirms once again that calculating resonances up to O (e2) suffices in order the overlap criterion to work out.
Facultad de Ciencias Astronómicas y Geofísicas
description Here we investigate the accuracy of the overlap criterion when applied to a simple near-integrable model in both its 2D and 3D versions. To this end, we consider, respectively, two and three quartic oscillators as the unperturbed system, and couple the degrees of freedom by a cubic, non-integrable perturbation. For both systems we compute the unperturbed resonances up to order O (e2), and model each resonance by means of the pendulum approximation in order to estimate the theoretical critical value of the perturbation parameter for a global transition to chaos. We perform several surface of sections for the bi-dimensional case to derive an empirical value to be compared to our theoretical estimation. Although both values are of the same order of magnitude, there is a significant difference between them. For the 3D case a numerical estimate is attained that we observe matches quite well the critical value resulting from theoretical means. This confirms once again that calculating resonances up to O (e2) suffices in order the overlap criterion to work out.
publishDate 2009
dc.date.none.fl_str_mv 2009
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/130649
url http://sedici.unlp.edu.ar/handle/10915/130649
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0020-7462
info:eu-repo/semantics/altIdentifier/arxiv/0807.2632
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.ijnonlinmec.2008.11.003
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
dc.format.none.fl_str_mv application/pdf
180-189
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instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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