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Israel Journal of Mathematics

, Volume 122, Issue 1, pp 1–27 | Cite as

Dynamical Borel-Cantelli lemmas for gibbs measures

  • N. Chernov
  • D. Kleinbock
Article

Abstract

LetT: X→X be a deterministic dynamical system preserving a probability measure μ. A dynamical Borel-Cantelli lemma asserts that for certain sequences of subsetsA n ⊃ X and μ-almost every pointx∈X the inclusionT n x∈A n holds for infinitely manyn. We discuss here systems which are either symbolic (topological) Markov chain or Anosov diffeomorphisms preserving Gibbs measures. We find sufficient conditions on sequences of cylinders and rectangles, respectively, that ensure the dynamical Borel-Cantelli lemma.

Keywords

Periodic Orbit Gibbs Measure Left Endpoint Markov Partition Topological Pressure 
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Copyright information

© Hebrew University 2001

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Alabama at BirminghamBirminghamUSA
  2. 2.Department of MathematicsRutgers UniversityPiscatawayUSA

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