Chaotic diffusion in the 2/1 asteroidal resonance An application of the frequency map analysis

We have applied the frequency map analysis of Laskar (1993) to the following dynamical models of the 2/1 asteroidal mean-motion resonance: the planar restricted threebody model and the planar restricted four-body model with Saturn. It allowed us to reproduce the chaotic region, which is formed by the overlap of secondary resonances in low eccentricities. We have examined the chaos generated by high-order secondary resonances in moderate eccentricities and concluded that, in the three-body planar model, most of the area remains regular even in the model with Jupiter’s eccentricity equal to 0.061. But, when the basic secular frequencies of Jupiter’s orbit were taken into account, themoderate-eccentricity region turned chaotic and a slow chaotic diffusion appeared. The diffusionwas found to be more significant in the full, planar four-bodymodel. Asteroids exhibited random excursions in the phase space and we studied this possible mechanism of resonance emptying in several 10-Myr integrations.