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arXiv · 2101.05586

On strong forms of the Borel--Cantelli lemma and intermittent interval maps

Andrei N. Frolov
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Abstract

We derive new variants of the quantitative Borel--Cantelli lemma and apply them to analysis of statistical properties for some dynamical systems. We consider intermittent maps of $(0,1]$ which have absolutely continuous invariant probability measures. In particular, we prove that every sequence of intervals with left endpoints uniformly separated from zero is the strong Borel--Cantelli sequence with respect to such map and invariant measure.

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Andrei N. Frolov. 2021-01-14. On strong forms of the Borel--Cantelli lemma and intermittent interval maps. https://arxiv.org/abs/2101.05586

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