Abstract
The utilization of chaotic dynamics approaches allowed the identification of many modes of motion in resonant asteroidal dynamics. As these dynamical systems are not integrable, the motion modes are not separated and one orbit may transit from one mode to another. In some cases, as in the 3/1 resonance, these transitions may lead, in a relatively short time scale, to eccentricities so high that the asteroid may approach the Sun and be destroyed. In the 2/1 and 3/2 resonances these transitions are much slower and only indirect estimations of the time which 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 those of the 3/2 resonance. These values are consistent with the observed depletion of the 2/1 resonance (only a few asteroids known while almost 60 asteroids are known in the 3/2 resonance).
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