The dynamical Borel-Cantelli lemma for interval maps

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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, then the dynamical Borel-Cantelli lemma does not hold even in the case that the map has a finite absolutely continuous invariant measure and summable decay of correlations.

Original languageEnglish
Pages (from-to)891-900
Number of pages10
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume17
Issue number4
DOIs
StatePublished - Apr 2007

Keywords

  • Maps with an indifferent fixed point
  • The dynamical Borel-Cantelli lemma

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