Diffusion characters of the orbits in the asteroid motion

A symplectic mapping is studied carefully. The exponential diffusion last, in developed chaotic region and algebraic law in mixed region were observed . An area was found where the diffusion follows a logarithmic law. It is sh own in the vicinity of an island, the logarithm of the escape time decrease s linearily as the initial position moves away from the island. But when ap proaching close to the island, the escape time goes up very quickly, consis tent with the superexponential stability of the invariant curve. When appli ed to the motion of asteroid, this mapping's fixed points and their stabili ties give an explanation of the distribution of asteroids. The diffusion ve locities in 4:3, 3:2 and 2:1 jovian resonances are also investigated.