| Abstract: |
| In this talk we discuss recent results concerning the return time statistics for deterministic and random dynamical systems. Taking the perturbative approach \`a la Keller-Liverani, we consider a decreasing sequence of holes in phase space which shrink to a point. For systems satisfying a spectral gap, we show that limiting distribution of return times to these shrinking holes is a compound Poisson distribution. We provide a specific example of a class of $\beta$-transformations for which the limiting distribution is the P\`olya-Aeppli distribution. |
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