Stefaan Vaes (KU Leuven)

Ergodic Theory Without Invariant Measures

Ergodic theory deals with dynamical systems from a measurable point of view. One considers transformations of a probability space, like the rotation of a circle over a typically irrational angle. In general, one considers transformations that may or may not preserve the given probability measure, but that will always preserve sets of measure zero. Iterating the transformation, one obtains a nonsingular action of the group of integers. A number of classification results for such nonsingular actions, and also for other groups than the integers, are introduced in this talk.