提升空间中的链传递性和强链回归点集的研究  

On Chain Transitive and Strong Chain Recurrent Point in the Lift Space

作　　者：冀占江 时伟 JI Zhan-jiang;SHI Wei(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;General Committee Office,Wuzhou Vocational College,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 [4]梧州职业学院党委办公室,广西梧州543002

出　　处：《西南师范大学学报（自然科学版）》2021年第8期47-50,共4页Journal of Southwest China Normal 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);梧州学院校级重点项目(2020B007);梧州学院校级项目(2017B004).

摘　　要：研究了局部等距条件下提升空间中链传递的动力学特征和强链回归点集的拓扑结构.利用局部等下提升映射的性质,得到链传递和强链回归点集的一些新结论:若映射是映射f局部等距下的提升映射,则是链传递当且仅当f是链传递;若映射是映射f局部等距下的提升映射,则π(SCR(f))■SCR(f).这些结论推广和改进了早期文献中关于链传递和强链回归点集的相关结果.The dynamical characteristics of chain transitive and the topological structure of strong chain recurrent point set are studied in the local equidistant lift space.With the property of the locally equidistant lift map,some new results of chain transitive and strong chain recurrent point set are obtained:If the map is the lift map of the map f under locally equidistant,then the map is chain transitive if and only if the map f is chain transitive;If the map is the lift map of the map f under locally equidistant,then we haveπ(SCR(f))■SCR(f).These conclusions generalize and improve the results of chain transitive and strong chain recurrent point set in the existing literature.

关 键 词：提升空间 等距映射 链传递 强链回归点集 

分 类 号：O189.11[理学—数学]