Testing the accuracy of the overlap criterion

dc.creatorMestre, Martín Federico
dc.creatorCincotta, Pablo Miguel
dc.creatorGiordano, Claudia Marcela
dc.date2009
dc.date2022-02-07T18:35:37Z
dc.date.accessioned2023-07-15T04:18:58Z
dc.date.available2023-07-15T04:18:58Z
dc.identifierhttp://sedici.unlp.edu.ar/handle/10915/130649
dc.identifierissn:0020-7462
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/7469078
dc.descriptionHere 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.
dc.descriptionFacultad de Ciencias Astronómicas y Geofísicas
dc.formatapplication/pdf
dc.format180-189
dc.languageen
dc.rightshttp://creativecommons.org/licenses/by/4.0/
dc.rightsCreative Commons Attribution 4.0 International (CC BY 4.0)
dc.subjectAstronomía
dc.subjectChaos
dc.subjectResonances
dc.subjectTheoretical and numerical method
dc.titleTesting the accuracy of the overlap criterion
dc.typeArticulo
dc.typeArticulo


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