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arXiv · 1603.08298

Note on limit distribution of normalized return times and escape rate

Xuan Zhang
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Abstract

In this note we discuss limit distribution of normalized return times for shrinking targets and draw a necessary and sufficient condition using sweep-out sequence in order for the limit distribution to be exponential with parameter $1$. The normalizing coefficients are the same as sizes of the targets. Moreover we study escape rate, namely the exponential decay rate of sweep-out sequence and prove that in $\psi$-mixing systems for a certain class of sets the escape rate is in limit proportional to the size of the set.

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Xuan Zhang. 2016-03-28. Note on limit distribution of normalized return times and escape rate. https://doi.org/10.1142/s0219493716600145

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