The dynamics of transitions between the cells of a finite-phase-space partition in a variety of systems giving rise to chaotic behavior is analyzed, with special emphasis on the statistics of recurrence times. In the case of one-dimensional piecewise Markow maps the recurrence problem is cast into a-renewal process. In the presence of intermittency, transitions between cells define a non-Markovian, non-renewal process reflected in the presence of power-law probability distributions and of divergent variances and mean values.
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Balakrishnan, V., Nicolis, G. & Nicolis, C. Recurrence time statistics in chaotic dynamics. I. Discrete time maps. J Stat Phys 86, 191–212 (1997). https://doi.org/10.1007/BF02180204
- Recurrence time
- escape time
- Markov partition
- fully developed chaos
- intermittent chaos