The critical dimension for G-measures
- Publication Type:
- Journal Article
- Ergodic Theory and Dynamical Systems, 2017, 37 (3), pp. 824 - 836
- Issue Date:
© 2015 Cambridge University Press. 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 G-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 G-measures.
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