Critical waiting time processes in infinite ergodic theory

Abstract

We study limit laws for return time processes defined on infinite conservative ergodic measure preserving dynamical systems. Especially for the critical cases with purely atomic limiting distribution we derive distorted processes posessing non-degenerated limits. For these processes also large deviation asymptotics are stated. The Farey map is used as an illustrating example giving new insides into the metric number theory of continued fractions.