The limiting distribution and error terms for return times of dynamical systems

We develop a new framework that allows to prove thatthe limiting distribution of return times for a large class ofmixing dynamical systems are Poissondistributed.We demonstrate our technique in several settings andobtain more general results than previously has been proven.We also obtain error estimates.For φ-mixing maps we obtain a close to exhausting descriptionof return times.For (φ,f)-mixing maps it is shown how the separation functionaffects error estimates for the limiting distribution.As examples of (φ,f)-mixing we prove that for piecewise invertiblemaps and for rational maps return times are in the limit Poisson distributed.