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

  • ANTHONY H. DOOLEY (a1) and RIKA HAGIHARA (a1)

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

  • ANTHONY H. DOOLEY (a1) and RIKA HAGIHARA (a1)

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