  We consider the return times dynamics to Bowen balls for continuous maps on
metric spaces which have invariant probability measures with certain mixing
properties. These mixing properties are satisfied for instance by systems that
allow Young tower constructions. We show that the higher order return times to
Bowen balls are in the limit Poisson distributed. We also provide a general
result for the asymptotic behavior of the recurrence time for Bowen balls for
ergodic systems and those with specification.
