强跟踪性和强链回归点集的研究  

The Research of Strong Shadowing Property and Strong Chain Recurrent Point Set

作　　者：冀占江 张更容 涂井先 JI Zhanjiang;ZHANG Gengrong;TU Jingxian(Wuzhou University School of Data Science and Software Engineering,Guangxi Wuzhou 543002,China;Wuzhou University Guangxi Colleges and Universities Key Laboratory of Image Processing and Intelligent Information System,Guangxi 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,长沙410205

出　　处：《河南大学学报（自然科学版）》2019年第6期739-744,共6页Journal of Henan University:Natural Science

基　　金：国家自然科学基金资助项目(11461002);湖南省自然科学基金资助项目(2018JJ2074);广西自然科学基金资助项目(2018JJB170034);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(2017C001)

摘　　要：研究了紧致度量空间中强跟踪性和强链回归点集的动力学性质,得到一些结论:(1)若f拓扑共轭于g,则连续映射f具有强跟踪性,当且仅当连续映射g具有强跟踪性;(2)连续映射g的强链回归点集是连续映射f的强链回归点集在拓扑共轭映射h下的像;(3)连续映射f^n的强链回归点集是连续映射f的强链回点集的子集;(4)移位映射σ的强链回归点集是连续映射f在它的强链回归点集上形成的逆极限空间的子集.这些结论推广和改进了目前已有文献中关于强跟踪性和强链回归点的结果.The dynamical properties of strong shadowing property and strong chain recurrent point set are studied in the compact metric spaces and some conclusions are obtained.(1) If the map f is topologically conjugate to the map g, then f has the strong shadowing property if and only if g has the strong shadowing property;(2) The strong chain recurrent point set of the continuous map g is the image of the strong chain recurrent point set of the continuous map f under the topological conjugate map h;(3)The strong chain recurrent point set of the the continuous map f^n is a subset of the strong chain recurrent point set of the the continuous map f;(4) The strong chain recurrent point sets of the shift map σ is a subset of the inverse limit space of the continuous map f in its strong chain recurrent point sets. These conclusions generalize and improve the results of strong shadowing property and strong chain recurrent point in the existing literature.

关 键 词：利普希茨映射 非游荡点 强链回归点 强跟踪性 

分 类 号：O189.11[理学—数学]