Dynamical Borel-Cantelli lemmas for Gibbs measures
نویسنده
چکیده
Let T : X 7→ X be a deterministic dynamical system preserving a probability measure μ. A dynamical Borel-Cantelli lemma asserts that for certain sequences of subsets An ⊂ X and μ-almost every point x ∈ X the inclusion Tnx ∈ An holds for infinitely many n. 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.
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تاریخ انتشار 1999