乘积G-空间中周期跟踪性和等度连续的研究  

The Research of Periodic Shadowing Property and Equicontinuity in the Product G-Space

作　　者：冀占江 张更容 涂井先 JI Zhan-jiang;ZHANG Geng-rong;TU Jing-xian(School of Data Science and Software Engineering, Wuzhou University, Wuzhou 543002, China;Guangxi Colleges and Universities Key Laboratory of Image Processing and Intelligent Information System, Wuzhou University, Wuzhou 543002, China;Mathematics and Computational Science, Hunnan First Normal University, Hunan 410205, 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]湖南第一师范学院数学与计算科学学院,湖南长沙 410205

出　　处：《数学的实践与认识》2019年第12期307-311,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11461002);湖南自然科学基金(2018JJ2074);广西自然科学基金(2016GXNSFAA380317,2018JJB170034);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：介绍了拓扑群作用下乘积空间中G-周期跟踪性和G-等度连续的概念,利用乘积映射的性质,研究了乘积映射/xg与分映射f和g在这些动力学性质方面的关系,得到如下结果:1)乘积映射fxg具有G-周期跟踪性当且仅当f具有Gi-周期跟踪性,g具有G2-周期跟踪性;2)乘积映射fxg具有G-等度连续当且仅当f具有Gi-等度连续,g具有G2-等度连续.这些结论弥补了拓扑群作用下乘积空间中G-周期跟踪性和G-等度连续理论的缺失.The concept of G-periodic shadowing property and G-equicontinuity is introduced in the product space under the action of topological group. By using the property of the product map, it is studied that the relationship of these dynamical properties between product mapping fxg and sub mapping /, g. It is gived that the following conclusions.(1) The product map fxg has the G-periodic shadowing property if and only if the map f has the Gi-periodic shadowing property and the map g has the ^-periodic shadowing property;(2) The product map fxg has the G-equicontinuity if and only if the map f has the G i -equicontinuity and the map g has the G?2-equicontinuity. These results enrich the theory of G-periodic shadowing property and G?equicontinuity in the product space under the action of topological group.

关 键 词：G-周期跟踪性 G-等度连续 乘积G-空间 乘积映射 

分 类 号：O189[理学—数学]