Testing the accuracy of the overlap criterion

MARTÍN MESTRE; PABLO CINCOTTA; CLAUDIA GIORDANO

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS

Elsevier

Lugar: Amsterdam; Año: 2009 vol. 44 p. 180 - 189

0020-7462

Here we investigate the accuracy of the overlap criterion when applied to a simple near-integrable modelin both its 2D and 3D versions. To this end,we consider,respectively,two and three quartic oscillatorsas 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 resonanceby means of the pendulum approximation in order to estimate the theoretical critical value of theperturbation parameter for a global transition to chaos.We perform several surface of sections for thebi-dimensional case to derive an empirical value to be compared to our theoretical estimation. Althoughboth values are of the same order of magnitude, there is a significant difference between them.For the3D case a numerical estimate is attained that we observe matches quite well the critical value resultingfrom theoretical means.This confirms once again that calculating resonances up to O(2) suffices in orderthe overlap criterion to work out