Measure-theoretic Entropy And Dynamical Properties For Free Semigroup Actions

This thesis studies measure-theoretic entropy and dynamical properties for free semigroup actions.We study some properties like conjugacy,power rule and affinity about the measure-theoretic entropy for a free semigroup action.This thesis includes two parts as follows:First part,we give some properties about measure-theoretic entropy for a free semigroup action like conjugacy,power rule and affinity.This is the extension of classical case.Second part,we introduce the notions of weak mixing and total transitivity for a free semigroup action.Let be a free semigroup acting on a compact metric space generated by continuous open self-maps.Assuming shadowing for ,we relate the average shadowing property to totally transitivity,topologically weak mixing,topological mixing,the specification property of by studying relationships between a free semigroup action and the skew product corresponding to the free semigroup action,thus we generalize the classical case to the case of free semigroup action.And we give some relative examples by these results.