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

Anthony H. Dooley, Rika Hagihara

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)103-117
Number of pages15
JournalErgodic Theory and Dynamical Systems
Volume32
Issue number01
Early online date4 Apr 2011
DOIs
Publication statusPublished - Feb 2012

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