Testing the accuracy of the overlap criterion

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 p...

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Autores principales: Mestre, Martín Federico, Cincotta, Pablo Miguel, Giordano, Claudia Marcela
Formato: Articulo
Lenguaje:Inglés
Publicado: 2009
Materias:
Astronomía
Chaos
Resonances
Theoretical and numerical method
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/130649
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-130649
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Astronomía
Chaos
Resonances
Theoretical and numerical method
spellingShingle Astronomía
Chaos
Resonances
Theoretical and numerical method
Mestre, Martín Federico
Cincotta, Pablo Miguel
Giordano, Claudia Marcela
Testing the accuracy of the overlap criterion
topic_facet Astronomía
Chaos
Resonances
Theoretical and numerical method
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.
format Articulo
Articulo
author Mestre, Martín Federico
Cincotta, Pablo Miguel
Giordano, Claudia Marcela
author_facet Mestre, Martín Federico
Cincotta, Pablo Miguel
Giordano, Claudia Marcela
author_sort Mestre, Martín Federico
title Testing the accuracy of the overlap criterion
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
publishDate 2009
url http://sedici.unlp.edu.ar/handle/10915/130649
work_keys_str_mv AT mestremartinfederico testingtheaccuracyoftheoverlapcriterion
AT cincottapablomiguel testingtheaccuracyoftheoverlapcriterion
AT giordanoclaudiamarcela testingtheaccuracyoftheoverlapcriterion
bdutipo_str Repositorios
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