V. Balakrishnan et al., RECURRENCE TIME STATISTICS IN CHAOTIC DYNAMICS .1. DISCRETE-TIME MAPS, Journal of statistical physics, 86(1-2), 1997, pp. 191-212
The dynamics of transitions between the cells of a finite-phase-space
partition in a variety of systems giving rise to chaotic behavior is a
nalyzed, with special emphasis on the statistics of recurrence times.
In the case of one-dimensional piecewise Markov maps the recurrence pr
oblem is cast into a renewal process. In the presence of intermittency
, transitions between cells define a non-Markovian, non-renewal proces
s reflected in the presence of power-law probability distributions and
of divergent variances and mean values.