Dynamics of Nonautonomous Discrete Dynamical Systems

Puneet Sharma, Manish Raghav

Published 2015-12-30Version 1

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 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. 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 an alternate criteria to establish weakly mixing/topological mixing for a non-autonomous dynamical system.