A systematic exploration of the chaotic structure of the asteroid belt is p
resented, first taking into account only the perturbations provided by the
four giant planets and then including also the effects of the inner planets
. We find that both the inner belt (a < 2.5 AU) and the outer part of the m
ain belt (a > 2.8 AU) are mostly chaotic. In the outer part of the belt, ch
aos is due to the presence of numerous mean-motion resonances with Jupiter
and three-body resonances, Jupiter-Saturn-asteroid. In the inner belt; chao
s is generated by mean motion resonances with Mars and three-body resonance
s, Mars-Jupiter-asteroid. Due to the chaoticity of the belt, asteroids tend
to slowly migrate in eccentricity. This phenomenon of "chaotic diffusion"
allows many bodies in the inner belt to become Mars-crossers. The number of
asteroids leaking out from the inner belt is large enough to keep the popu
lation of Mars-crossing asteroids in steady state, despite of the short dyn
amical lifetime of the latter (similar to 25 Myr). We speculate that chaoti
c diffusion could have substantially eroded the high-eccentricity part of t
he asteroid belt, thus providing the impactors responsible for the Late Hea
vy Bombardment phase of the early Solar System. (C) 1999 Academic Press.