title: Superdiffusion in the dissipative standard map.
abstract: 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 for the cases when a control parameter is close to some special values that correspond to the ballistic mode dynamics. Diffusion near the related crises is anomalous and nonuniform 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 nonchaotic 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.
authors.affiliation: Department of Physics, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, New York 10012, USA.
authors.forename: G M
authors.initials: GM
authors.lastname: Zaslavsky
authors.forename: M
authors.initials: M
authors.lastname: Edelman
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008962:Models, Theoretical; D017711:Nonlinear Dynamics