Topological R-entropy And Topological Entropy Of Free Semigroup Actions

This thesis studies topological r-entropy and topological entropy of free semigroup actions on a compact metric space.This thesis includes two parts as follows:First part,we introduce the notion of topological r-entropy of free semigroup actions and obtain some properties of it on a compact metric space.Then,we give the relationship between topological r-entropy and topological entropy of free semigroup actions.That is,the topological entropy of free semigroup actions,in the sense of Bufetov,is the limit of topological r-entropy(r?0).Second part,we verify that the topological entropy of f0,…,fm-1 equals the topo-logical entropy of f0-1,…,fm-1-1,by using the skew-product transformation as bridge.It answers a question raised by Wang,Ma and Lin in[40].