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Quantitative Uniform Hitting in Exponentially Mixing Systems

  • Ai Hua Fan
  • Thomas Langlet
  • Bing Li
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Summary

Consider an exponentially mixing metric measure preserving system \((X,\mathcal{B},\mu,T,d)\). Let αmax be the maximal local dimension of μ. It is proved that if τ < 1 ∕ αmax, then for μ-almost all x and for every yX we have lim inf\(_{n \to \infty } n^\tau d(T^n x,y) = 0\). The critical value 1 ∕ αmax is optimal in many cases.

Keywords

Gibbs Measure Cantelli Lemma Pointwise Dimension Measure Preserve System Gibbs Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.LAMFA, UMR 6140, CNRSUniversité de PicardieAmiensFrance

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