SECULAR RESONANCES IN MEAN MOTION COMMENSURABILITIES - THE 4 1, 3/1, 5/2, AND 7/3 CASES/

With this paper we complete our review on the dynamics in mean motion resonances. Here we investigate the 4/1, 3/1, 5/2, and 7/3 commensurab ilities and show that, due to the interaction between the nu(5) and nu (6) secular resonances, chaotic motion is present almost everywhere in the phase space. This chaotic motion is responsible for the large jum ps in the eccentricity (up to 0.8 or more) that one usually observes i n the realistic numerical simulations, which force the asteroids to cr oss the orbits not only of Mars, but even of Earth. In this way we ach ieve a better understanding of the effective mechanisms for the deplet ion of the 3/1, 5/2, and 4/1 resonances, and we are able to explain, f or the first time, the existence of the gap associated with the 7/3 me an motion commensurability. (C) 1995 Academic Press, Inc.