Diffusion Character in Four-Dimensional Volume-Preserving Map

Due to the existence of invariant tori, chaotic sea and hyperbolic structures in higher dimensional phase space of a volume-preserving map, the diffusion route of chaotic orbits will be complicated. The velocity of diffusion will be very slow if the orbits are near an invariant torus. In order to realize this complicated diffusion phenomenon, in this paper we study the diffusion characters in the different regions, i.e., chaotic, hyperbolic and invariant tori's regions. We find that for the three different regions, the diffusion velocities are different. The diffusion velocity in the vicinity of an invariant torus is the slowest one. This revised version was published online in July 2006 with corrections to the Cover Date.