Computing the critical dimensions of Bratteli-Vershik systems with multiple edges

The critical dimension is an invariant that measures the growth rate of the sums of Radon-Nikodym derivatives for non-singular dynamical systems. We show that for Bratteli-Vershik systems with multiple edges, the critical dimension can be computed by a formula analogous to the Shannon-McMillan-Breiman theorem. This extends earlier results of Dooley and Mortiss on computing the critical dimensions for product and Markov odometers on infinite product spaces. © Cambridge University Press 2011