The Properties And Calculation Of Directional Preimage Entropy For Z_+~k-actions

Dynamical system is a mathematical branch that studies the behavior of the time-varying system.In the study of the complexity of the systems,entropy plays a very important role.In order to get a comprehensive understanding of the system,many types of entropies are introduced and studied from different points of view.In this paper,directional preimage entropy for Z_+~k-actions is introduced and its properties are studied.Moreover,the calculation of this type of entropy is considered for several classical Z_+~k-actions.The contents of the thesis mainly include three parts.In the first part,a new type of entropy,directional preimage entropy for Z_+~k-actions,is introduced by using spanning set and separated set.In the second part,the properties of directional preimage entropy for Z_+~k-actions are investigated.Some relationships among these entropies and the invariance of these entropies under topological conjugation are obtained.In the third part,several systems including Z_+~k-actions generated by the expand-ing maps,Z_+~k-actions defined on a finite graph and some infinite graph that have zero directional preimage branch entropy are studied.