G-跟踪性和G-周期跟踪性研究  

The research on G-shadowing property and G-periodic shadowing property

作　　者：冀占江 JI Zhanjiang(School of Data Science and Software Engineering,Wuzhou University,Wuzhou 543002,Guangxi Zhuang Autonomous Region,China;Guangxi Key Laboratory of Machine Vision and Intelligent Control,Wuzhou University,Wuzhou 543002,Guangxi Zhuang Autonomous Region,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]梧州学院广西机器视觉与智能控制重点实验室,广西梧州543002

出　　处：《浙江大学学报（理学版）》2023年第4期429-433,共5页Journal of Zhejiang University（Science Edition）

基　　金：广西自然科学基金资助项目(2018JJB170034,2020JJA110021);广西高校中青年教师科研基础能力提升项目(2019KY0681);梧州学院校级重点项目(2020B007)。

摘　　要：研究了度量G-空间中G-跟踪性与G-周期跟踪性之间的动力学关系,给出了G-跟踪性和G-周期跟踪性的定义,利用等价映射和伪等价映射的性质,得到:(1)设(X,d)为紧致度量G-空间,G为可交换的紧致群,f:X→X等价,若f具有G-周期跟踪性,则P_(G)(f)=CR_(G)(f)(2);设(X,d)为紧致度量G-空间,G为紧致群,f:X→X等价,若f具有G-跟踪性且P_(G)(f)=W_(G)(f),则f具有G-周期跟踪性;(3)设(X,d)为紧致度量G-空间,G为可交换的紧致群,f:X→X伪等价,若f为G-扩张映射且f具有G-跟踪性,则f具有G-周期跟踪性。所得结论推广了度量空间中跟踪性和周期跟踪性的相关结论。The dynamical relationship between G-shadowing property and G-periodic shadowing property is studied in metric G-space.The definitions of G-shadowing property and G-periodic shadowing property are given.By using the properties of equivalent mapping and pseudo equivalent mapping,the following results are obtained:(1)let(X,d)be compact metric G-space,G be commutative and compact group and f:X→X be an equivariant map.If f has G-periodic shadowing property,then P_(G)(f)=CR_(G)(f);(2)let(X,d)be compact metric G-space,G be compact group and f:X→X be an equivariant map.If f has G-shadowing property and P_(G)(f)=W_(G)(f),then f has G-periodic shadowing property;(3)let(X,d)be compact metric G-space,G be commutative and compact group and f:X→X be a pseudo equivariant map.If f is G-expansive map and f has G-shadowing property,then f has G-periodic shadowing property.These results generalize the conclusions of shadowing property and periodic shadowing property in metric spaces.

关 键 词：G-跟踪性 G-周期跟踪性 G-链回归点 G-扩张映射 

分 类 号：O189.11[理学—数学]