The dynamical Borel-Cantelli lemma for interval maps

Abstract

The dynamical Borel-Cantelli lemma for some interval maps is considered.For expanding maps whose derivative has bounded variation, any sequence of intervals satisfies the dynamical Borel-Cantelli lemma.If a map has an indifferent fixed point, thenthe dynamical Borel-Cantelli lemma does not hold even in the case that the map has a finite absolutely continuous invariant measureand summable decay of correlations.