Computing the critical dimensions of Bratteli-Vershik systems with multiple edges
- Publication Type:
- Journal Article
- Ergodic Theory and Dynamical Systems, 2012, 32 (1), pp. 103 - 117
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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.
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