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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:504

Article

Frolov, Andrei N.¹ 

[1] St Petersburg State Univ, Dept Math & Mech, St Petersburg, Russia

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

DOI  :  10.1016/j.jmaa.2021.125425

来源: Elsevier

【 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.

【 授权许可】

Free