A symplectic mapping approach of the dynamics of the Hecuba gap

In this work, we develop a symplectic mapping allowing the study of the dynamical behavior of asteroidal resonances. To obtain such a mapping, we combine the symplectic scheme proposed by Hadjidemetriou together with an asymmetric expansion of the disturbing function which takes into account the inclinations of both the perturber and the disturbed bodies. This mapping is applied 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 the diffusion mechanisms acting in these resonances.