Chaotic Characteristics in Devaney's Framework for Set-Valued Discrete Dynamical Systems

This paper focuses on the relationship between a non-autonomous discrete dynamical system (NDDS) (H,f1,infinity) and its induced set-valued discrete dynamical systems (K(H),f over bar 1,infinity). Specifically, it explores the chaotic properties of these systems. The main finding is that f1,infinity is Devaney chaotic if and only if f over bar 1,infinity is Devaney chaotic in we-topology. The paper also provides similar conclusions for weak mixing, mixing, mild mixing, chain-transitivity, and chain-mixing in non-autonomous set-valued discrete dynamical systems (NSDDSs). Additionally, the paper proves that weak mixing implies sensitivity in NSDDSs.