Topological entropy of generalized discrete dynamical system

Abstract

In this paper, the authors introduce Bowen’s topological entropy for generalized discrete dynamical system. This is achieved through the consideration of the generalized spanning sets and generalized separated sets. Besides, we obtain that our definition keeps some properties which are held by the classic definition of topological entropy introduced for metric sets. Finally, we further discuss the relations of the generalized spanning set and generalized separated set between systems and their product system. These results further extend the scope of the research on discrete dynamical system and generalize the existing results to a very general case.