Universiteit Utrecht

Department of Mathematics

σ - finite measure preserving transformations and Young towers

Henk Bruin
(Surrey University (UK))

3 June 2009

Dynamical systems that preserve an infinite σ - finite invariant measure (absolutely continuous to Lebesgue) appear naturally, e.g., in the presence of neutral fixed points (Manneville-Pomeau map and various higher-dimensional maps emerging from continued fraction algorithms) and also in the logistic family. The ergodic properties that one can derive for such measures are of a quite different order than those of invariant probability measures. In this talk I want to show how the Young tower construction (based on jump-transformations with good distortion control) can be used as a general tool to address the ergdoic properties for σ - finite measures. This work is joint with Dalia Terhesiu (Surrey) and Matt Nicol (Houston).

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Alexandra Babenko