群作用下逆极限空间和乘积空间中的强G-跟踪性  

The Strong G-shadowing Property of the Inverse Limit Spaces and the Product Spaces of Group Action

作　　者：冀占江 张更容 涂井先 JI Zhanjiang;ZHANG Gengrong;TU Jingxian(School of Data Science and Software Engineering∥Guangxi Colleges and Universities Key Laboratory of Image Processing and Intelligent Information System,Wuzhou University,Wuzhou 543002,China;School of Mathematics and Computational Science,Hunan First Normal University,Changsha 410205,China)

机构地区：[1]梧州学院大数据与软件工程学院∥广西高校图像处理与智能信息系统重点实验室,梧州543002 [2]湖南第一师范学院数学与计算科学学院,长沙410205

出　　处：《华南师范大学学报（自然科学版）》2019年第6期103-106,共4页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11461002);湖南省自然科学基金项目(2018JJ2074);广西自然科学基金项目(2018JJB170034);广西高校中青年教师科研基础能力提升项目(2019KY0681);梧州学院校级科研项目(2017C001)

摘　　要：给出了拓扑群作用下度量空间中强G-跟踪性的概念,研究了拓扑群作用下逆极限空间和乘积空间中强G-跟踪性的动力学性质,得到如下结论:(1)若(Xf,■,■,σ)是系统(X,G,d,f)的逆极限空间,则f具有强G-跟踪性当且仅当σ具有强■-跟踪性;(2) f1×f2具有强G-跟踪性当且仅当f1具有强G1-跟踪性,f2具有强G2-跟踪性.这些结论弥补了拓扑群作用下逆极限空间和乘积空间中强G-跟踪性理论的缺失.The concept of the strong G-shadowing property is given in the metric spaces under the action of topological group. Then the dynamical properties of the strong G-shadowing property in the inverse limit spaces and the product spaces under the action of topological group are studied. The following conclusions are obtained. Let the system( Xf,■,■,σ) be the inverse limit spaces of the system( X,G,d,f). Then f has the G-shadowing property if and only if σ has the ■-shadowing property. The product map f1× f2 has the strong G-shadowing property if and only if the map f1 has the strong G1-shadowing property and the map f2 has the strong G2-shadowing property. These results enrich the theory of strong G-shadowing property in the inverse limit spaces and the product spaces under the action of topological group.

关 键 词：G-跟踪性 强G-跟踪性 逆极限空间 乘积空间 

分 类 号：O189.11[理学—数学]