Quantitative Uniform Hitting in Exponentially Mixing Systems

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


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.


Gibbs Measure Cantelli Lemma Pointwise Dimension Measure Preserve System Gibbs Property 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

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

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