Statistical properties of equilibrium states for rational maps

Equilibrium states of rational maps for Holder continuous potentials are no t mixing, mainly due to the presence of critical points. Here we prove that for disks the normalized return times of arbitrary orders are, in the limi t, Poisson distributed as the radius of the disks go to zero. The return ti mes are normalized by the measure of the disks. We also show that rational maps are weakly Bernoulli with respect to the partition given by Denker and Urbanski.