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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/130649
Ver los metadatos del registro completo
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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 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://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 |
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http://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International (CC BY 4.0) |
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application/pdf 180-189 |
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SEDICI (UNLP) - Universidad Nacional de La Plata |
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