Metric Entropy of Nonautonomous Dynamical Systems

TL;DR

This paper generalizes the classical metric entropy concept to nonautonomous dynamical systems, establishing foundational properties and linking it to topological entropy, thus broadening the understanding of entropy in evolving systems.

Contribution

It introduces a new notion of metric entropy for nonautonomous systems, extending classical theory and proving key properties like invariance, a power rule, and inequalities.

Findings

Defines metric entropy for nonautonomous systems

Establishes invariance under isomorphisms

Proves a power rule and a Rokhlin-type inequality

Abstract

We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence of probability spaces and a sequence of measure-preserving maps between these spaces. 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.