Minimal rates of entropy convergence for completely ergodic systems
type: Item
instance of: scholarly article
title: Minimal rates of entropy convergence for completely ergodic systems
zbMATH Open document ID: 0939.37005
DOI: 10.1007/BF02783038
author: Frank Blume
published in: Israel Journal of Mathematics
publication date: 2000-07-06T00:00:00Z
review text: Let \((X,{\mathcal B},m,T)\) be a completely ergodic measure-preserving dynamical system. It is shown that for some diverging positive sequence \(\{a_n:n\geq 1\}\) and some positive concave function \(g\) \(\liminf_{n \to\infty} H(\alpha_0^{n-1}) /a_n>0\) and \(\limsup_{n\to \infty}H (\alpha_0^{n-1})/g (\log_2n)>0\) for all nontrivial two set partitions of \(X\). This work continues the author investigations in [Ergodic Theory Dyn. Syst. 17, 45-70 (1997; Zbl 0891.28012)].
reviewed by: Manfred Denker
Mathematics Subject Classification ID: 37A35
Mathematics Subject Classification ID: 37A25
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 28D20
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 1270345
zbMATH Keywords: measure theoretic entropy
zbMATH Keywords: completely ergodic
zbMATH Keywords: rank one transformations
MaRDI profile type: Publication
cites work: Cutting and stacking, interval exchanges and geometric models
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cites work: Cutting and stacking: a method for constructing stationary processes
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cites work: Universal redundancy rates for the class of B-processes do not exist
full work available at URL: https://doi.org/10.1007/bf02783038
OpenAlex ID: W2083961799
description: scientific article; zbMATH DE number 1270345