有限生成群作用的Gromov-Hausdorff跟踪性  

Gromov-Hausdorff shadowing property for finitely generated group actions

作　　者：刘鑫磊 董美花[1] LIU Xinlei;DONG Meihua(College of Science,Yanbian University,Yanji 133002,China)

机构地区：[1]延边大学理学院,吉林延吉133002

出　　处：《延边大学学报（自然科学版）》2023年第4期308-309,340,共3页Journal of Yanbian University（Natural Science Edition）

基　　金：国家自然科学基金(12201541);吉林省教育厅科学技术研究规划项目(612021001)。

摘　　要：将Gromov-Hausdorff跟踪性(G-H跟踪性)和等距跟踪性的概念推广到了紧致度量空间上的有限生成群作用,并利用类比推理的方法得到如下结果:若群作用具有伪轨跟踪性,则其具有GH跟踪性;若群作用具有GH跟踪性,则其具有等距跟踪性.该结果可为研究拓扑动力系统的跟踪性提供参考.The concepts of Gromov-Hausdorff shadowing property(GH-shadowing property)and isometric shadowing property were extended to finite generated group actions on compact metric spaces,and the following results were obtained using analogical reasoning:if the group action has the pseudo-orbit tracing property,it has GH-shadowing property;if the group action has GH-shadowing property,then it has isometric shadowing property.This result can provide a reference for the shadowing property research of topological dynamical systems.

关 键 词：Gromov-Hausdorff跟踪性 等距跟踪性 群作用 伪轨跟踪性 紧致空间 

分 类 号：O192[理学—数学]