Limit laws for distorted return time processes for infinite measure preserving transformations

Mathematics – Dynamical Systems

Scientific paper

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18 pages, 2 figures

Scientific paper

10.1142/S0219493707001962

We consider conservative ergodic measure preserving transformations on infinite measure spaces and investigate the asymptotic behaviour of distorted return time processes with respect to sets satisfying a type of Darling-Kac condition. We identify two critical cases for which we prove uniform distribution laws. For this we introduce the notion of uniformly returning sets and discuss some of their properties.

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