Malaysian Journal of Mathematical Sciences, May 2022, Vol. 16, No. 2


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

Wong, K. S. and Salleh, Z.

Corresponding Email: zabidin@umt.edu.my

Received date: 30 May 2020
Accepted date: 16 February 2022

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.

Keywords: set-valued dynamical systems; sensitive; topologically transitive; topologically mixing; product dynamical systems.