LIU Xinlei,DONG Meihua.Gromov - Hausdorff shadowing property for finitely generated group actions[J].Journal of Yanbian University,2023,(04):308-309,340.
有限生成群作用的Gromov - Hausdorff跟踪性
- Title:
- Gromov - Hausdorff shadowing property for finitely generated group actions
- 文章编号:
- 1004-4353(2023)04-0308-03
- 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
- Keywords:
- Gromov - Hausdorff hadowing property; isometric shadowing property; group action; pseudo - orbit tracing property; compact metric space
- 分类号:
- O192
- 文献标志码:
- A
- 摘要:
- 将Gromov - Hausdorff跟踪性(GH- 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.
- Abstract:
- 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.
参考文献/References:
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备注/Memo
收稿日期: 2023-10-08
基金项目: 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)
第一作者: 刘鑫磊(1998—),男,硕士研究生,研究方向为拓扑动力系统.
通信作者: 董美花(1982—),女(朝鲜族),博士,副教授,研究方向为拓扑动力系统.