An Exploration Of Certain Properties Of Chaotic Dynamics In G-Spaces

Abstract

Let X be a topological G-space and let Ϝ_n (X) be the n-fold symmetric product of X, for any positive integer n. Let f∶ X→ X be a function, we consider the induced functions Ϝ_n(f): Ϝ_n(X) → Ϝ_n(X). In this paper we presented some chaotic properties like: Transitive, Mixing, Weakly Mixing, Totally Transitive, Exact, Strongly Transitive and Chaotic. We investigate the relationship between systems f and Ϝ_n (f) for the above properties.