强一致收敛下渐进周期点和逐点跟踪性的研究  

The research of asymptotically periodic point and pointwise shadowing property under strongly uniform convergence

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

出　　处：《安徽大学学报（自然科学版）》2019年第4期36-39,共4页Journal of Anhui University(Natural Science Edition)

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：在强一致收敛条件下研究了序列映射与极限映射之间关于渐进周期性和逐点跟踪性的关系,利用强一致收敛和等度连续的性质,得到如下结果:(1)设序列映射{fn}强一致收敛于等度连续映射f且点列{xk}是每个映射fn的渐进周期点,若limk→∞xk=x,则x是f的渐进周期点;(2)若序列映射{fn}强一致收敛于等度连续映射f,则limsupAPer(fn)APer(f);(3)设序列映射{fn}强一致收敛于f,若fn具有fine逐点跟踪性,则f具有逐点跟踪性。The relationship of the asymptotically periodic property and pointwise shadowing property between the sequence map and the limit map under strongly uniform convergence was studied. By using the properties of the strong uniform convergence and equicontinuity,the following results were obtained:(1) Supposed that the sequence map {f n} converged strongly uniformly to the equicontinuous map f and the sequence of points {x k} be the asymptotically periodic point of every map f n, if lim k→∞ x k=x ,then the point x was the asymptotically periodic point of the map f;(2) If the sequence map {f n} converged strongly uniformly to the equicontinuous map f ,then lim sup A Per (f n) A Per (f);(3) Supposed that the sequence map {f n} converged strongly uniformly to the map f, if f n had the fine pointwise shadowing property,then f had pointwise shadowing property.

关 键 词：渐进周期点 逐点跟踪性 等度连续 强一致收敛 

分 类 号：O189[理学—数学]