Chaotic Characteristics in Devaney’s Framework for Set-Valued Discrete Dynamical Systems - Jie Zhou; Tianxiu Lu; Jiazheng Zhao (Axioms, 2023)
This paper focuses on the relationship between a non-autonomous discrete dynamical system (NDDS) <semantics>(H,f1,∞)</semantics> and its induced set-valued discrete dynamical systems <semantics>(K(H),<mover accent="true">f¯</mover>1,∞)</semantics>. Specifically, it explores the chaotic properties of these systems. The main finding is that <semantics>f1,∞</semantics> is Devaney chaotic if and only if <semantics><mover accent="true">f¯</mover>1,∞</semantics> is Devaney chaotic in <semantics>we</semantics>-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.