群作用下逆极限空间中移位映射的动力学性质  

Dynamical properties of the shift map in the inverse limit space of group action

作　　者：冀占江 覃桂茳 张更容[3] JI Zhanjiang;QIN Guijiang;ZHANG Gengrong(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;School of Mathematics and Computer 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,湖南长沙410205

出　　处：《安徽大学学报（自然科学版）》2020年第5期41-45,共5页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11461002);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：相关文献研究了逆极限空间中周期点集、极限点集和回归点集的动力学性质,得到了比较好的结果.借鉴相关方法,考虑群作用下逆极限空间中G-周期点集、G-极限点集和G-回归点集的动力学性质,得到如下结果:(1)移位映射的G-周期点集等于自映射在其G-周期点集上形成的逆极限空间;(2)移位映射的G-极限点集等于自映射在其G-极限点集形成的逆极限空间;(3)移位映射的G-回归点集等于自映射在其G-回归点集形成的逆极限空间.这些结果进一步丰富了群作用下逆极限空间中的理论.Related literature studied the dynamical properties of periodic point sets,limit point sets and recurrent point sets in the inverse limit space and obtained some good results.Based on the above method,it is discussed that dynamical property of G-periodic point sets,G-limit point sets and G-recurrent point sets in the inverse limit space of group action.The following results were obtained:(1)G-periodic point sets of the shift map were equal to the inverse limit space of the self mapping in the G-periodic point sets.(2)G-limit point sets of the shift map were equal to the inverse limit space of the self mapping in the G-limit point sets.(3)G-recurrent point sets of the shift map were equal to the inverse limit space of the self mapping in the G-recurrent point sets.These results enriched the theory of the inverse limit space of group action.

关 键 词：逆极限空间 移位映射 G-周期点集 G-极限点集 G-回归点集 

分 类 号：O189.11[理学—数学]