真映射生成半群的拓扑压  

The Topological Pressure of a Semigroup Action Generated by Proper Maps

作　　者：张文杰 杨荣领 Zhang Wen-jie;Yang Rong-ling(School of Mathematics,South China University of Technology,Guangzhou 510641,China;Guangzhou College,South China University of Technology,Guangzhou 510800,China)

机构地区：[1]华南理工大学数学学院,广东广州510641 [2]华南理工大学广州学院,广东广州510800

出　　处：《广东工业大学学报》2020年第3期59-62,共4页Journal of Guangdong University of Technology

基　　金：国家自然科学基金资助项目(11671149);广东省自然科学基金资助项目(2014A030313230);中央高校基础研究基金资助项目(SCUT(2015ZZ055,2015ZZ127))。

摘　　要：在Bis和Patrao定义的拓扑熵基础上给出了度量空间中有限个真映射构成的半群的拓扑压,并证明了局部紧可分度量空间上由真映射构成的自由半群的拓扑压和它的一点紧化空间上对应的拓扑压相等,在此基础上给出真映射构成的半群的拓扑压的性质。As an extension of topological entropy,topological pressure was first proposed by Ruelle in 1973,and then further extended by Walters to compact metric spaces of continuous maps.It reflects the complexity of dynamic system,and it is an important research content in fractal geometry and dynamic system.In order to solve more complex problems relevant to topological pressure,more and more new research has emerged.On the basis of the topological entropies defined by Bis and Patrao,the topological pressure of a semigroup action generated by proper maps of the metric space is given,and then the topological pressure of a free semigroup action generated by proper maps in a locally compact separable metric space is proved,which is equivalent to the topological pressure of a free semigroup action in its one-point compactification space.Furthermore,some properties of the topological pressure of a free semigroup action are given.

关 键 词：拓扑压 自由半群 真映射 度量空间 

分 类 号：O189.1[理学—数学]