Dynamics of Nonautonomous Discrete Dynamical Systems

TL;DR

This paper investigates the complex behaviors of non-autonomous discrete dynamical systems generated by families of continuous maps, providing conditions for properties like chaos, mixing, and entropy on compact spaces.

Contribution

It establishes necessary and sufficient conditions for complex behaviors in non-autonomous systems and highlights differences from autonomous systems.

Findings

Conditions for transitivity, mixing, and chaos in non-autonomous systems

Examples showing non-autonomous behavior cannot be deduced solely from generating functions

Analysis of topological entropy and Li-Yorke chaos in these systems

Abstract

In this paper we study the dynamics of a general non-autonomous dynamical system generated by a family of continuous self maps on a compact space $X$. We derive necessary and sufficient conditions for the system to exhibit complex dynamical behavior. In the process we discuss properties like transitivity, weakly mixing, topologically mixing, minimality, sensitivity, topological entropy and Li-Yorke chaoticity for the non-autonomous system. We also give examples to prove that the dynamical behavior of the non-autonomous system in general cannot be characterized in terms of the dynamical behavior of its generating functions.