Dimension and waiting time in rapidly mixing systems

Abstract

We prove that if a system has superpolynomial (faster than any power law) decay of correlations then the time ${\tau }_r(x,x_0)$ 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. $$\underset{r\to 0}{\lim }\frac{\log {\tau }_r(x,x_0)}{-\log r}=d_{\mu }(x_0).$$

Revised version, very similar to the one is published

References in corpus (1)

• The dynamical Borel-Cantelli lemma and the waiting time problems

Cited by in corpus (1)

• Long hitting time, slow decay of correlations and arithmetical properties