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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access July 10, 2013

Metric Entropy of Nonautonomous Dynamical Systems

  • Christoph Kawan EMAIL logo

Abstract

We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence (Xn; μn) of probability spaces and a sequence of measurable maps fn : Xn → Xn+1 with fnμn = μn+1. This notion generalizes the classical concept of metric entropy established by Kolmogorov and Sinai, and is related via a variational inequality to the topological entropy of nonautonomous systems as defined by Kolyada, Misiurewicz, and Snoha. Moreover, it shares several properties with the classical notion of metric entropy. In particular, invariance with respect to appropriately defined isomorphisms, a power rule, and a Rokhlin-type inequality are proved

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Received: 2013-5-24
Accepted: 2013-6-24
Published Online: 2013-7-10
Published in Print: 2014-1-1

© 2013 Christoph Kawan

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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