Renewal theory and statistics of rare events in infinite ergodic theory

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This research project is dedicated to the investigation of dynamical systems, in particular to the study of infinite ergodic theory. These systems can be characterized as being chaotic (e.g. the dynamic returns typically infinitely often to small sets), but the return time to a given set might be extremely large. It is intended to develop qualitative and quantitative statistical description of the dynamics with the help of functional analytic renewal methods applied to the so-called transfer operator. In particular we are interested to develop extreme value statistics for return times.