English

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

Probability 2021-01-15 v1 Dynamical Systems

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](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.

Keywords

Cite

@article{arxiv.2101.05586,
  title  = {On strong forms of the Borel--Cantelli lemma and intermittent interval maps},
  author = {Andrei N. Frolov},
  journal= {arXiv preprint arXiv:2101.05586},
  year   = {2021}
}