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A Borel-Cantelli lemma for intermittent interval maps

Sebastien Gouezel
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Abstract

We consider intermittent maps T of the interval, with an absolutely continuous invariant probability measure μ. Kim showed that there exists a sequence of intervals A_n such that \sum μ(A_n)=\infty, but \{A_n\} does not satisfy the dynamical Borel-Cantelli lemma, i.e., for almost every x, the set \{n : T^n(x)\in A_n\} is finite. If \sum \Leb(A_n)=\infty, we prove that \{A_n\} satisfies the Borel-Cantelli lemma. Our results apply in particular to some maps T whose correlations are not summable.

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Sebastien Gouezel. 2007-03-09. A Borel-Cantelli lemma for intermittent interval maps. https://doi.org/10.1088/0951-7715%2F20%2F6%2F010

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