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Updated: Jun 27, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Superdiffusion in the dissipative standard map
1Department of Physics, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, New York 10012, USA.
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.
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