Appears in collection : Extreme value theory and laws of rare events / Théorie des valeurs extrêmes et lois des évènements rares

It is shown that for systems that allow a Young tower construction with polynomially decaying correlations the return times to metric balls are in the limit Poisson distributed. The error terms are powers of logarithm of the radius and so is the size of the forbidden set which one has to exclude. In particular it shows that the return times to balls is Poissonian for SRB measures on attractors.