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

Reference:

Dooley, A. H. and Hagihara, R., 2012. Computing the critical dimensions of Bratteli–Vershik systems with multiple edges. Ergodic Theory and Dynamical Systems, 32 (01), pp. 103-117.

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Official URL:

http://dx.doi.org/10.1017/S0143385710000969

Abstract

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.

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