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.