Open AccessTopologically Transitive and Mixing Properties of Set-Valued Dynamical Systems
Author(s) -
Koon Sang Wong,
Zabidin Salleh
Publication year - 2021
Publication title -
abstract and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.228
H-Index - 56
eISSN - 1687-0409
pISSN - 1085-3375
DOI - 10.1155/2021/5541105
Subject(s) - mathematics , transitive relation , mixing (physics) , dynamical systems theory , set (abstract data type) , equivalence (formal languages) , dynamical system (definition) , pure mathematics , topological conjugacy , discrete mathematics , combinatorics , computer science , physics , quantum mechanics , programming language
We introduce and study two properties of dynamical systems: topologically transitive and topologically mixing under the set-valued setting. We prove some implications of these two properties for set-valued functions and generalize some results from a single-valued case to a set-valued case. We also show that both properties of set-valued dynamical systems are equivalence for any compact intervals.