Systems with chaotic dynamics possess anomalous statistical properties, and their trajectories do not correspond to the Gaussian process. This property imposes description of such time characteristics as the distribution of exit times or Poincarérecurrences by introducing a (multi-) fractal time scale in order to satisfy the observed powerlike tails of the distributions. We introduce a corresponding phase-space-time partitioning and spectral function for dimensions, and make a connection between dimensions and transport exponent that defines the anomalous ('strange') kinetics.

• Received 25 November 1996

DOI:https://doi.org/10.1103/PhysRevE.55.5418