乘积度量G-空间中强跟踪性和极限跟踪性的研究  

The Research on Strong Shadowing Property and Limit Shadowing Property in the Product Metric G-Space

作　　者：冀占江 时伟 JI Zhan-jiang;SHI Wei(School of Data Science and Software Engineering,Wuzhou University,Wuzhou 543002,Guangxi,China;Guangxi Colleges and Universities Key Laboratory of Image Processing and Intelligent Information System,Wuzhou University,Wuzhou 543002,Guangxi,China;Wuzhou Vocational College,Wuzhou 543002,Guangxi,China)

机构地区：[1]梧州学院大数据与软件工程学院,广西梧州543002 [2]梧州学院广西高校图像处理与智能信息系统重点实验室,广西梧州543002 [3]梧州职业学院,广西梧州543002

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2020年第3期189-193,共5页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：广西自然科学基金资助项目(2018JJB170034);广西高校中青年教师科研基础能力提升资助项目(2019KY0681);梧州学院校级科研资助项目(2017C001)。

摘　　要：引入拓扑群作用下乘积空间中G-跟踪性、G-强跟踪性和G-极限跟踪性的概念,结合乘积映射的性质,研究了乘积映射f×g与分映射f和g在这些跟踪性方面的关系,得到如下结论:(1)乘积映射f×g具有G-跟踪性当且仅当f具有G1-跟踪性,g具有G2-跟踪性;(2)乘积映射f×g具有G-强跟踪性当且仅当f具有G1-强跟踪性,g具有G2-强跟踪性;(3)乘积映射f×g具有G-极限跟踪性当且仅当f具有G1-极限跟踪性,g具有G2-极限跟踪性。这些结论弥补了拓扑群作用下乘积空间中强跟踪性和极限跟踪性理论的缺失。We introduced the concept of G-shadowing property,G-strong shadowing property and G-limit shadowing property in the product space under the action of topological group.By means of properties of the product map,the relationship in these shadowing properties between product mapping f×g and sub mapping f,g were studied.The following conclusions were obtained:(1)The product map f×g had the G-shadowing property if and only if the map f had the G1-shadowing property and the map g had the G2-shadowing property;(2)The product map f×g had the G-strong shadowing property if and only if the map f had the G1-strong shadowing property and the map g had the G2-strong shadowing property;(3)The product map f×g had the G-limit shadowing property if and only if the map f had the G1-limit shadowing property and the map g had the G2-limit shadowing property.The conclusions made some supplements for the theory of strong shadowing property and limit shadowing property in the product space under the action of topological group.

关 键 词：G-跟踪性 G-强跟踪性 G-极限跟踪性 乘积映射 

分 类 号：O189.11[理学—数学]