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Artículo

Testing the accuracy of the overlap criterion

Mestre, Martin FedericoIcon ; Cincotta, Pablo MiguelIcon ; Giordano, Claudia MarcelaIcon
Fecha de publicación: 03/2009
Editorial: Pergamon-Elsevier Science Ltd
Revista: International Journal Of Non-linear Mechanics
ISSN: 0020-7462
Idioma: Inglés
Tipo de recurso: Artículo publicado
Clasificación temática:
Astronomía

Resumen

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(2), 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(2) suffices in order the overlap criterion to work out.
Palabras clave: Chaos , Resonances , Numerical Methods , Theoretical Methods
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info:eu-repo/semantics/openAccess Excepto donde se diga explícitamente, este item se publica bajo la siguiente descripción: Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Unported (CC BY-NC-SA 2.5)
Identificadores
URI: http://hdl.handle.net/11336/42820
DOI: http://dx.doi.org/10.1016/j.ijnonlinmec.2008.11.003
URL: https://www.sciencedirect.com/science/article/pii/S0020746208001868?via%3Dihub
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Articulos(IALP)
Articulos de INST.DE ASTROFISICA LA PLATA
Citación
Mestre, Martin Federico; Cincotta, Pablo Miguel; Giordano, Claudia Marcela; Testing the accuracy of the overlap criterion; Pergamon-Elsevier Science Ltd; International Journal Of Non-linear Mechanics; 44; 2; 3-2009; 180-189
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