度量G-空间中G-链回归点的G-链等价集  

G-chain Equivalent Set of G-chain Recurrent Point in the Metric G-space

作　　者：冀占江 粟光旺 JI Zhan-jiang;SU Guang-wang(School of Information and Electronic 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;Department of Mathematics and Statistics,Guangxi University of Finance and Economics,Nanning 530003,China)

机构地区：[1]梧州学院信息与电子工程学院,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]广西财经学院信息与统计学院,广西南宁530003

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2019年第3期210-215,共6页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：广西自然科学基金资助项目(2016GXNSFBA380235);广西高校中青年教师科研基础能力提升项目(2019KY0681);广西高校中青年教师基础能力提升项目(2017KY0598);硕士学位授予单位立项建设项目(桂学位[2013]4号);梧州学院科校级研项目(2017C001)

摘　　要：根据链回归点和链等价点的定义,给出了G-链回归点和G-链等价点的概念,并研究了度量G-空间中G-链回归点集和G-链等价集的动力学性质,得到如下结果:(1)映射f的G-链回点集等于映射f^n的G-链回归点集;(2)点x关于映射f^n的G-链等价集等于点f^n(x)关于映射f^n的G-链等价集;(3)点x关于映射f的G-链等价集等于集合■;(4)集合CE_G(f^i(x),f^n)在映射f作用下的象等于点f^(i+1)(x)关于映射f^n的G-链等价集.所得结果丰富了度量G-空间中G-链回归点集和G-链等价集的理论.The concepts of G-chain recurrent point and G-chain equivalent point were derived according to the definition of chain recurrent point and chain equivalent point.In addition,we studied the dynamical properties of G-chain recurrent point set and G-chain equivalent set in the metric G-space and obtained the following result:(1)The G-chain recurrent point set of the mapping f is equal to G-chain recurrent point set of the mapping f n;(2)The G-chain equivalent set of the point x with respect to the mapping f n is equal to the G-chain equivalent set of the point f n(x)with respect to the mapping f n;(3)The G-chain equivalent set of the point x with respect to the mapping f is equal to the set∪n-1 i=0 C E G(f i(x),f n);(4)The image of the set C E G(f i(x),f n)under the mapping f is equal to the G-chain equivalent set of the point f i+1(x)with respect to the mapping f n.These conclusions enrich the theory of G-chain recurrent point set and G-chain equivalent set in the metric G-space.

关 键 词：度量G-空间 拓扑群 伪等价映射 G-链回归点 G-链等价点 

分 类 号：O189.11[理学—数学]