Tony Dooley
Title: Critical dimension and non-singular ergodic theory

Abstract: In a non-singular dynamical system, the rate of growth of the partial sums of Radon-Nikodym derivatives gives an invariant which we call the critical dimension. In the case of Product or Markov odometers, this is related to the average coordinate entropy. It is an invariant for metric isomorphism. Recent results show that the ciritical dimension of an induced transformation on a subset of positive measure is related to the original critical dimension. The natural orbit equivalenceswhich preserve critical dimension are called Hurewicz equivalences. I shall discuss the conjecture that the critical dimension classifies systems up to Hurewicz equivalence.