强一致收敛下几乎周期点和逐点周期跟踪性的动力学性质  

Dynamical properties of almost periodic point andpointwise periodic shadowing property under strongly uniform convergence

作　　者：冀占江 张更容 JI Zhan-jiang;ZHANG Geng-rong(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：《东北师大学报（自然科学版）》2020年第2期30-34,共5页Journal of Northeast Normal 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).

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几乎周期性和逐点周期跟踪性的关系,所得结果对强一致收敛下几乎周期点和逐点周期跟踪性理论的发展有一定的促进作用.It is studied that the relationship of the almost periodic property and pointwise periodic shadowing property between the sequence map and the limit map under strongly uniform convergence.By using the properties of the strong uniform convergence and equicontinuity,the following results are obtained.Let the sequence map{f n}converges strongly uniformly to the equicontinuous map f and the sequence of points{x k}be the almost periodic point of every map f n.If lim k→∞x k=x,then the point x is the almost periodic point of the mapf;If the sequence map{f n}converges strongly uniformly to the equicontinuous map f,then limsup AP(f n)AP(f);Let the sequence map{f n}converges strongly uniformly to the map f.If f n has the fine pointwise periodic shadowing property,then f has pointwise periodic shadowing property.These results have the positive effect on the development of the theory of the almost periodic property and pointwise periodic shadowing property under strongly uniform convergence.

关 键 词：几乎周期点 逐点周期跟踪性 强一致收敛 等度连续 

分 类 号：O189.11[理学—数学]