Abstract
We briefly summarize the progresses of the last decade in our understanding of the dynamics of asteroids inside the mean motion resonances with Jupiter, from the very simplified model of the averaged planar circular restricted three body problem, to some very realistic models including the effects of several planets. For most of the simple commensurabilities, chaotic motion leads to high eccentricities which lead to planet crossing, which lead to removal of the asteroid. For the 2:1 commensurability, the result is not so clear and still controversial.
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