CONSTRUCTION OF A NEKHOROSHEV LIKE RESULT FOR THE ASTEROID BELT DYNAMICAL SYSTEM

We investigate the possibility of obtaining a Nekhoroshev like result for the dynamical system describing the motion of an asteroid in the m ain belt. From the mathematical point of view this is a new result sin ce the problem is degenerate and we want to control also the motion of degenerate actions. We find that there are regions, such as the reson ances of low order among the fast angles (mean motion resonances), whe re a Nekhoroshev like result cannot be proved a priori. Conversely, we are able to confine the motions in the mean motion resonances of loga rithmically large order in the perturbation parameters, as well as in the non-resonant region. We discuss also the connection with the exist ence of invariant tori.