A SYMPLECTIC MAPPING APPROACH TO THE STUDY OF THE STOCHASTICITY IN ASTEROIDAL RESONANCES

In the case of the 2:1 and 3:2 resonances with Jupiter, it has not bee n yet possible to have a complete identification of all chaotic diffus ion processes at work, mainly because the time scale of some of them a re of an order still out of the reach of precise integrations. A plana r Hadjidemetriou's mapping, using expansions valid for high eccentrici ties and scaled in order to accelerate the diffusion processes, was de rived. The solutions obtained with the mapping show huge eccentricity variations in all orbits starting in the middle of the 2:1 resonance, when the main short-period perturbations of Jupiter's orbit are consid ered. The solutions starting in the middle of the 3:2 resonance do not show any important diffusion.