2 00 8 Dimension and hitting time in rapidly mixing systems

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 a typical point x to enter for the first time a ball B(x 0 , r) centered in x 0 , with small radius r scales as the local dimension at x 0 , i.e. lim r→0 log τ r (x, x 0) − log r = d µ (x 0). This result is obtained by proving a kind of dynamical Borel-Cantelli lemma wich holds also in systems having polinomial decay of correlations.