Weak mixing and chaos in nonautonomous discrete systems

The paper is devoted to a study of chaotic properties of nonautonomous discrete systems (NDS) defined by a sequence f ∞ = { f i } i = 0 ∞ of continuous maps acting on a compact metric space. We consider such properties as chaos in the sense of Li and Yorke, topological weak mixing and topological entropy, all defined in a way suitable for NDS. We compare these concepts with the case of a single map (discrete dynamical system, DS for short) and relate them to recent results in the topic. While previous research of various authors were focusing on analogues to the DS case, we show that in general the dynamics of NDSs is much richer and quite different than what is expected from the DS case. We also provide a few new tools that can be used for the successful investigation of their qualitative behavior.