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.
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.
作者
金秋实
董美花
JIN Qiushi;DONG Meihua(College of Science,Yanbian University,Yanji 133002,China)
出处
《延边大学学报（自然科学版）》
CAS
2023年第2期126-128,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)。
关键词
测度可扩
强测度可扩
不变测度
Borel概率测度
群作用
周期点
measure expansive
strong measure expansive
invariant measure
Borel probability measure
group action
periodic point
