提升空间中渐近平均跟踪性和链回归点的研究  

The research of asymptotic average shadowing property and chain recurrent point in the lift space

作　　者：冀占江 贝彩霞 张更容 JI Zhan-jiang;BEI Cai-xia;ZHANG Geng-rong(School of Data Science and Software Engineering,Guangxi Colleges and Universities Key Laboratory of Image Processing and Intelligent Information System,Guangxi Colleges and Universities Key Laboratory of Professional Software Technology,Wuzhou University,Wuzhou 543002,China;School of Health Profession,Wuzhou Vocational College,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,广西高校图像处理与智能信息系统重点实验室,广西高校行业软件技术重点实验室,广西梧州543002 [2]梧州职业学院卫生健康学院,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）》2022年第2期22-26,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(2020JJA110021);广西高校中青年教师科研基础能力提升项目(2019KY0681)。

摘　　要：研究了提升空间中渐近平均跟踪性和链回归点的动力学性质,在局部等距提升映射的作用下,利用等距映射的性质得到如下结论:(1)f^(-1)具有渐近平均跟踪性,当且仅当f具有渐近平均跟踪性;(2)π(CR(f^(-))■CR(f).这些结果丰富了提升空间中渐近平均跟踪性和链回归点的理论.The dynamical properties of asymptotic average shadowing property and chain recurrent point are studied in the lift space.By using the property of the equidistant map,some conclusions are obtained under the local equidistant lift map.First,the map f^(-1) has the asymptotic average shadowing property if and only if the map f has the asymptotic average shadowing property.Second,π(CR(f^(-1))■CR(f).These results enrich the theory of asymptotic average shadowing property and chain recurrent point in the lift space.

关 键 词：提升空间 等距映射 渐近平均跟踪性 链回归点 

分 类 号：O189.11[理学—数学]