关于连续映射半群拓扑熵的一点注记  

A REMARK ON THE TOPOLOGICAL ENTROPY OF A SEMIGROUP OF CONTINUOUS MAPS

作　　者：田延国 马东魁[1] TIAN Yan-guo;MA Dong-kui(School of Mathematics, South China University of Technology, Guangzhou, 510641, China)

机构地区：[1]华南理工大学数学学院,广东广州510641

出　　处：《数学杂志》2017年第4期792-796,共5页Journal of Mathematics

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

摘　　要：本文研究了度量空间中连续映射构成半群的拓扑熵.利用Patr′ao^([8])的方法,给出了度量空间中两种有限个连续映射构成的半群的拓扑d-熵的定义,比较了两种拓扑d-熵的大小.证明了局部紧致可分度量空间上有限个真映射构成的半群的拓扑d-熵和它的一点紧化空间上对应的拓扑熵相等.上面结果推广了Patr′ao的相应结论.In this paper,we study the topological entropy of a semigroup of continuous maps on a metric space.By using Patrao's[8]method,we give two de finitions of topological dentropy of a semigroup generated by finite continuous maps on a metric space,the size of these two d-entropies are compared.We also show that the topological dentropy of the semigroup generated by finite proper maps on a locally compact separable metric space and the topological entropy on its one-point compactification space coincide,which extend the results obtained by Patrao.

关 键 词：拓扑熵 半群 真映射 度量空间 

分 类 号：O189.1[理学—数学]