IALP   13078
INSTITUTO DE ASTROFISICA LA PLATA
Unidad Ejecutora - UE
artículos
Título:
Testing the accuracy of the overlap criterion
Autor/es:
MESTRE, M.; CINCOTTA, P.M.; GIORDANO, C.M:
Revista:
International Journal of Non-Linear Mechanics
Editorial:
Elsevier
Referencias:
Año: 2008 vol. 44 p. 179 - 188
ISSN:
0020_7462
Resumen:
Here we investigate the accuracy of the overlap criterion when applied to a simple near-integrable model in both its 2D and 3D version.To this end, we consider, respectively, two and three quartic oscillators as the unperturbed system, and couple the degree of freedom by a cubic non-integrable perturbation. For both systems we compute the unperturbed resonances up to order O(epsilon²), and model each resonance by means of a 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(epsilon²) suffices in order the overlap criterion to work out.