半群作用的传递紧  

Transitive compactness of semigroup action

作　　者：杨霄 李华海 钟新林 YANG Xiao;LI Hua-hai;ZHONG Xin-lin(School of Mathematics and Information Science,Guangzhou University,Guangzhou 510006,China)

机构地区：[1]广州大学数学与信息科学学院,广东广州510006

出　　处：《广州大学学报（自然科学版）》2023年第6期86-92,共7页Journal of Guangzhou University:Natural Science Edition

摘　　要：文章主要研究了半群作用的动力系统中的传递紧以及它与其他传递性之间的关联。主要结果如下:①当S是一个交换半群时,若(S,X)是弱混合,则(S,X)是传递紧;②若(S,X)是弹性的,则(S,X)是完全传递的;③当S是一个交换半群时,n-传递(n≥2)、弱混合和弹性是等价的。This paper studies transitive compactness and its relationships with other forms of transitivi-ty for dynamical systems with semigroup actions.Main results are as follows:if(S,X)is weakly mixing where S is an Abelian semigroup,then(S,X)is transitively compact;②if(S,X)is elastic,then(S,X)is completely transitive;③we prove that n-transitivity(n≥2),weakly mixing and elas-tic are equivalent mutually when S is an Abelian semigroup.

关 键 词：传递紧 弱混合 弹性 n-传递 

分 类 号：O189.11[理学—数学]