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.

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