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 language | English |
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Pages (from-to) | 891-900 |
Number of pages | 10 |
Journal | Discrete and Continuous Dynamical Systems- Series A |
Volume | 17 |
Issue number | 4 |
DOIs | |
State | Published - Apr 2007 |
Keywords
- Maps with an indifferent fixed point
- The dynamical Borel-Cantelli lemma