Fractal and multifractal properties of exit times and Poincare recurrences

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 Poincare recurrences by introducing a (multi-) fractal timescale 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.