Dimension and hitting time in rapidly mixing systems

• DOI: 10.4310/mrl.2007.v14.n5.a8
• Publication Date: 2013-08-30T23:46:25Z
• Authors: Stefano Galatolo
• Keywords: Lemma (botany); Ball (mathematics)

We prove that if a system has superpolynomial (faster than any power law) decay of correlations then the time τ r (x, x 0 ) needed for typical point to enter first ball B(x , r) centered in with small radius scales as local dimension at i.e.This result is obtained by proving kind dynamical Borel-Cantelli lemma wich holds also systems having polinomial correlations.