Superdiffusion in the Dissipative Standard Map

We consider transport properties of the chaotic (strange) attractor along unfolded trajectories of the dissipative standard map. It is shown that the diffusion process is normal except of the cases when a control parameter is close to some special values that correspond to the ballistic mode dynamics. Diffusion near the related crisises is anomalous and non-uniform in time: there are large time intervals during which the transport is normal or ballistic, or even superballistic. The anomalous superdiffusion seems to be caused by stickiness of trajectories to a non-chaotic and nowhere dense invariant Cantor set that plays a similar role as cantori in Hamiltonian chaos. We provide a numerical example of such a sticky set. Distribution function on the sticky set almost coincides with the distribution function (SRB measure) of the chaotic attractor.