乘积G-空间的G-极小性、G-混合性和G-链回归点  

G-MINIMALITY,G-MIXING AND G-CHAIN RECURRENT POINT OF THE PRODUCT G-SPACE

作　　者：冀占江 张更容 JI Zhan-jiang;ZHANG Geng-rong(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,Changsha 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：《数学杂志》2019年第3期399-404,共6页Journal of Mathematics

基　　金：国家自然科学基金资助(11461002);湖南自然科学基金资助(2018JJ2074);广西自然科学基金资助(2016GXNSFAA380317);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资助(2017C001)

摘　　要：本文研究了拓扑群作用下乘积空间中G-极小性、G-混合性和G-链回归点的动力学问题.利用乘积映射与分映射之间的方法,获得如下结果:(1)乘积映射f×g是G-极小映射当且仅当f是G_1-极小映射,g是G_2-极小映射;(2)乘积映射f×g是G-混合映射当且仅当f是G_1-混合映射,g是G_2-混合映射;(3) CR_G(f×g)=CR_(G_1)(f)×CR_(G_2)(g).从而推广了乘积空间中极小性、混合性和链回归点的结果.In this paper,the dynamical problem of G-minimality property,G-mixing property and G-chain recurrent point are investigated in the product space under the action of topological group.By using the method between product mapping and sub mapping,the following results are obtained.(1)The product map f×g is a G-minimality map if and only if the map f is a G1-minimality map and the map g is a G2-minimality map;(2)The product map f×g is a G-mixing map if and only if the map f is a G1-mixing map and the map g is a G2-mixing map;(3)CRG(f×g)=CRG1(f)×CRG2(g),which generalize the results of minimality property,mixing property and chain recurrent point in the product space.

关 键 词：G-极小性 G-混合性 G-链回归点 乘积G-空间 

分 类 号：O189.11[理学—数学]