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

Published online by Cambridge University Press:  05 April 2011

ANTHONY H. DOOLEY  and
RIKA HAGIHARA
ANTHONY H. DOOLEY
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia (email: a.dooley@unsw.edu.au, r.hagihara@unsw.edu.au)
RIKA HAGIHARA
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia (email: a.dooley@unsw.edu.au, r.hagihara@unsw.edu.au)
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 1 , February 2012 , pp. 103 - 117
Copyright
Copyright © Cambridge University Press 2011

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