A symplectic mapping approach of the dynamics of the Hecuba gap

In this work, we develop a symplectic mapping allowing the study of the dyn amical behavior of asteroidal resonances. To obtain such a mapping, we comb ine the symplectic scheme proposed by Hadjidemetriou together with an asymm etric expansion of the disturbing function which takes into account the inc linations of both the perturber and the disturbed bodies. This mapping is a pplied to the 2/1 and 3/2 mean motion resonances in the asteroidal belt. We explore a wide range of initial conditions in the phase space in order to get a large number of results to allow some statistical conclusions about t he diffusion mechanisms acting in these resonances. (C) 1999 Elsevier Scien ce Ltd. All rights reserved.