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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.

Details

Item Type Articles
CreatorsDooley, A. H.and Hagihara, R.
DOI10.1017/S0143385710000969
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code32433

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