Dynamical Borel-Cantelli lemmas for Gibbs measures

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dc.creatorChernov, Nikolai
dc.creatorKleinbock, Dmitry
dc.date1999-12-21
dc.date.accessioned2026-07-07T05:32:25Z
dc.date.available2026-07-07T05:32:25Z
dc.descriptionLet $T: X\mapsto X$ be a deterministic dynamical system preserving a probability measure $μ$. A dynamical Borel-Cantelli lemma asserts that for certain sequences of subsets $A_n\subset X$ and $μ$-almost every point $x\in X$ the inclusion $T^nx\in A_n$ 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.
dc.descriptionLatex, 22 pages
dc.identifierhttps://arxiv.org/abs/math/9912178
dc.identifierhttp://arxiv.org/abs/math/9912178
dc.identifierIsrael J. Math. 122 (2001), 1--27.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79651
dc.subjectDynamical Systems
dc.subject37B10, 37D20
dc.titleDynamical Borel-Cantelli lemmas for Gibbs measures
dc.typetext

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