Three-body mean motion resonances and the chaotic structure of the asteroid belt

We discuss the existence and the properties of a new type of mean motion re sonance populated by a large number of asteroids, the resonant angle being defined as a linear combination (with integer coefficients) of the mean lon gitudes of asteroid, Jupiter, and Saturn. We call these resonances the thre e-body mean motion resonances. In the present paper, we show that the anoma lous large oscillation of the mean semimajor axis of about 250 numbered ast eroids is associated with some of the most prominent three-body mean motion resonances, and we conjecture that the actual number of the resonant aster oids is much larger. The positive Lyapunov exponent detected for the majori ty of resonant bodies in our numerical integrations suggests the chaotic na ture of their orbits. Moreover, we show, using frequency analysis, that orb its in the three-body mean motion resonances may slowly and chaotically dif fuse in eccentricity. The existence of such diffusion may have major conseq uences for our present understanding of the long-term evolution of the aste roidal belt and the delivery of objects to near-Earth orbits.