Dynamical Borel-Cantelli lemmas for gibbs measures | Zendy

N. Chernov | Zendy; Dmitry Kleinbock | Zendy

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Dynamical Borel-Cantelli lemmas for gibbs measures

Author(s) -

N. Chernov,

Dmitry Kleinbock

Publication year - 2001

Publication title -

israel journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.168

H-Index - 63

eISSN - 1565-8511

pISSN - 0021-2172

DOI - 10.1007/bf02809888

Subject(s) - mathematics , lemma (botany) , markov chain , dynamical systems theory , probability measure , discrete mathematics , dynamical system (definition) , measure (data warehouse) , pure mathematics , combinatorics , statistics , computer science , ecology , physics , poaceae , quantum mechanics , database , biology

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.

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