Diffusion in a Symplectic Map with Application to Asteroid Motion

In studying a 2-dimensional syrnplectic map, the exponential law and algebraic law are observed in the diffusion of orbits in the phase space. The diffusion time in the vicinity of an island is investigated carefully and a logarithm law is found for the first time. The distribution of asteroids in the main belt and the diffusion velocities in 3:2 and 4:3 resonances are discussed using this map.