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

[摘要] 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. (c) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-15

[关键词] Borel-Cantelli lemma;Intermittent interval maps;Non-uniformly hyperbolic dynamical systems