G-强跟踪性和利普希茨跟踪性的研究  

Research of G-Strong Shadowing Property and Lipschitz Shadowing Property

作　　者：冀占江 JI Zhanjiang(School of Data Science and Software Engineering,Wuzhou University,Wuzhou Guangxi 543002,China;Guangxi Colleges and Universities Key Laboratory of Image Processing and Intelligent Information System,Wuzhou University,Wuzhou Guangxi 543002,China;Guangxi Colleges and Universities Key Laboratory of Professional Software Technology,Wuzhou University,Wuzhou Guangxi 543002,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]梧州学院广西高校行业软件技术重点实验室,广西梧州543002

出　　处：《西南大学学报（自然科学版）》2022年第4期128-133,共6页Journal of Southwest University(Natural Science Edition)

基　　金：广西自然科学基金面上项目(2020JJA110021);广西自然科学基金项目(2018JJB170034);广西高校中青年教师科研基础能力提升项目(2021KY0679);梧州学院校级重点项目(2020B007).

摘　　要：给出了G-强跟踪性和利普希茨跟踪性的定义,分别在度量G-空间和无限乘积空间中研究了它们的动力学性质,得到如下结果:在度量G-空间中对任意的正整数k≥2,f具有G-强跟踪性当且仅当f^(k)具有G-强跟踪性;在无限乘积空间X中移位映射σ具有利普希茨跟踪性.这些结论丰富了度量G-空间和无限乘积空间中的相关理论.The definitions of G-strong shadowing property and Lipschitz shadowing property are given,and their dynamical properties are respectively studied in metric G-space and infinite product space.The results are as follows:For any positive integer k≥2,the map f has G-strong shadowing property if and only if the map f^(k) has G-strong shadowing property in metric G-space;The shift mapσhas Lipschitz shadowing property in infinite product space X.These results enrich the theory of metric G-space and infinite product space.

关 键 词：度量G-空间 移位映射 G-强跟踪性 利普希茨跟踪性 

分 类 号：O189.11[理学—数学]