Classification of non-singular systems and critical dimension
Anthony Dooley (University of Bath)
Tuesday 26th November, 2013 16:00-17:00 Maths 416
In work with Hamachi, I have shown that every non-singular measurable dynamical system is orbit equivalent to a Markov odometer on a Bratteli-Vershik system which is uniquely ergodic, minimal and induced as a subsystem of a full odometer. At the same time, Mortiss and I introduced a new invariant, the critical dimension, for metric isomorphism of non-singular systems: it is given by the rate of growth of sums of Radon-Nikodym derivatives. The critical dimension induces a natural form of equivalence between systems, which we call Hurewicz equivalence. It turns out that the critical dimension is an invariant for Hurewicz equivalence of Markov odometers of finite width, and this leads to a classification theorem.