Uniform Convergence, Mixing and Chaos

Abstract

Let (X, d) be a compact metric space and let f_n : X → X be a sequence of continuous maps such that {f_n} converges uniformly to a continuous and surjective map f: X → X. Weinvestigate the elements of topological mixing and the chaotic behavior possessed by f_n that can be inherited by f.Key Words: Topological mixing; Weakly topological mixing; Distributional chaos in a sequence; Uniform convergence