Dynamical Borel-Cantelli lemmas for gibbs measures |
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Authors: | N Chernov D Kleinbock |
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Institution: | (1) Department of Mathematics, University of Alabama at Birmingham, 35294 Birmingham, AL, USA;(2) Department of Mathematics, Rutgers University, 08854 Piscataway, NJ, USA |
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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.
Partially supported by NSF grant DMS-9732728.
Partially supported by NSF grant DMS-9704489. |
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Keywords: | |
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