Abstract

The critical dimension of an ergodic non-singular dynamical system is the asymptotic growth rate of sums of consecutive Radon–Nikodým derivatives. This has been shown to equal the average coordinate entropy for product odometers when the size of individual factors is bounded. We extend this result to (Formula presented.)-measures with an asymptotic bound on the size of individual factors. Furthermore, unlike von Neumann–Krieger type, the critical dimension is an invariant property on the class of ergodic (Formula presented.)-measures.

Original languageEnglish
Pages (from-to)824-836
JournalErgodic Theory and Dynamical Systems
Volume37
Issue number3
Early online date21 Oct 2015
DOIs
Publication statusPublished - May 2017

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Radon
Critical Dimension
Dynamical systems
Entropy
Radon-Nikodym Derivative
Derivatives
Consecutive
Dynamical system
Invariant
Class

Cite this

The critical dimension for G-measures. / Mansfield, Daniel F.; Dooley, Anthony H.

In: Ergodic Theory and Dynamical Systems, Vol. 37, No. 3, 05.2017, p. 824-836.

Research output: Contribution to journalArticle

Mansfield, Daniel F. ; Dooley, Anthony H. / The critical dimension for G-measures. In: Ergodic Theory and Dynamical Systems. 2017 ; Vol. 37, No. 3. pp. 824-836.
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