Dynamical entropy for Markov operators
type: Item
instance of: scholarly article
title: Dynamical entropy for Markov operators
zbMATH Open document ID: 0973.37006
DOI: 10.1023/A:1009595020696
author: I. I. Makarov
published in: Journal of Dynamical and Control Systems
publication date: 2000-10-22T00:00:00Z
review text: The author defines and examines the entropy for the class of Markov operators, an intermediate case between the classical and quantum systems. The author proves that in the case \(Pf(x)= f(Tx)\), where \(T\) is a measure preserving transformation and \(P\) is a Markov operator, the newly defined entropy coincides with the Kolmogorov-Sinai entropy of \(T\). Moreover the author studies a dilation of the Markov operator \(P\) through the Markov chain associated with \(P\). It is shown that the entropy depends on the projections \(\pi_{-\infty}\) and \(\pi_0\) on \(\sigma\)-algebras \({\mathcal A}_{-\infty}\) and \({\mathcal A}_0\) of the Markov chain.
Mathematics Subject Classification ID: 37A30
Mathematics Subject Classification ID: 28D20
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 60J05
Mathematics Subject Classification ID: 37A50
zbMATH DE Number: 1475289
zbMATH Keywords: entropy
zbMATH Keywords: Markov operator
zbMATH Keywords: measure preserving transformation
zbMATH Keywords: Markov chain
zbMATH Keywords: quantum system
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1475289