  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.
$$\underset{r\to 0}{\lim}\frac{\log \tau_{r}(x,x_{0})}{-\log r}=d_{\mu
}(x_{0}).$$
