JIN Qiushi,DONG Meihua.Measure expansivity and strong measure expansivity for group actions[J].Journal of Yanbian University,2023,(02):126-128.
群作用的测度可扩性和强测度可扩性
- Title:
- Measure expansivity and strong measure expansivity for group actions
- Keywords:
- measure expansive; strong measure expansive; invariant measure; Borel probability measure; group action; periodic point
- 分类号:
- O192
- 文献标志码:
- A
- 摘要:
- 利用类比的方法将测度可扩和强测度可扩的概念从同胚推广到了紧致度量空间上的群作用,并证明了群作用下的测度可扩是动力性质.另外,还证明了没有周期点的群作用T 是测度可扩当且仅当其是强测度可扩,以及如果群作用T 是强测度可扩的,则T|Per(T)是可扩的.
- Abstract:
- The concepts of measure expansive and strong measure expansive were extended from homeomorphism to group action on compact metric space by analogy.And it was proved that measure expansive under group action was a dynamic property.In addition, it was also proved that group action T without periodic points was measure expansive if and only if it was strong measure expansive and if group action T was strong measure expansive, then T|Per(T) was expansive.
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备注/Memo
收稿日期: 2023 04 13
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: 金秋实(1999—),女,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,博士,副教授,研究方向为拓扑动力系统.