Some Properties on Sensitivity, Transitivity and Mixing of Set-Valued Dynamical Systems

Abstract

In this paper, we study the dynamical properties of set-valued dynamical systems. Specifically, we focus on the sensitivity, transitivity and mixing of set-valued dynamical systems. Under the setting of set-valued case, we define sensitivity and investigate its properties. We also study the transitivity and mixing of set-valued dynamical systems that have been defined. We show that both transitivity and mixing are invariant under topological conjugacy. We also discuss some implication results on the product set-valued function constructed from two different set-valued functions equipped with various transitivity and mixing conditions.