Metric Entropy of Nonautonomous Dynamical Systems

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.