有限生成群作用的Gromov-Hausdorff跟踪性

Gromov-Hausdorff shadowing property for finitely generated group actions

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.