A Note on Topological Entropy of Continuous Self-Maps

Abstract

Topological entropy can be an indicator of complicated behavior in dynamical systems. It is first introduce by Adler, Konheim and McAndrew by using open covers in 1965. After that it is still an active research by many researchers to produce more properties and applications up to nowadays. The purpose of this paper is to review and explain most important concepts and results of topological entropies of continuous self-maps for dynamical systems on compact and non-compact topological and metric spaces. We give proofs for some of its elementary properties of the topological entropy. Slight modification on Adler's topological entropy is also presented.