CHAOTIC TRANSITIONS IN RESONANT ASTEROIDAL DYNAMICS

The utilization of chaotic dynamics approaches allowed the identificat ion of many modes of motion in resonant asteroidal dynamics. As these dynamical systems are not integrable, the motion modes are not separat ed and one orbit may transit from one mode to another. In same cases, as in the 3/1 resonance, these transitions may lead, in a relatively s hort time scale, to eccentricities so high that the asteroid may appro ach the Sun and be destroyed. In the 2/1 and 3/2 resonances these tran sitions are much slower and only indirect estimations of the time whic h is needed for a generic asteroid to leave the resonance are possible . It may reach hundreds of million years in the more robust regions of the 2/1 resonance and a time of the order of billions of years in tho se of the 3/2 resonance. These values are consistent with the observed depletion of the 2/1 resonance (only a few asteroids known while almo st 60 asteroids are known in the 3/2 resonance).