Equicontinuity and Sensitivity of Group Actions  

作　　者：Shaoting XIE Jiandong YIN 

机构地区：[1]Department of Mathematics,Nanchang University,Nanchang 330031,China

出　　处：《Chinese Annals of Mathematics,Series B》2023年第4期501-516,共16页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.12061043,11661054)。

摘　　要：Let(X,G)be a dynamical system(G-system for short),that is,X is a topological space and G is an infinite topological group continuously acting on X.In the paper,the authors introduce the concepts of Hausdorff sensitivity,Hausdorff equicontinuity and topological equicontinuity for G-systems and prove that a minimal G-system(X,G)is either topologically equicontinuous or Hausdorff sensitive under the assumption that X is a T_(3)-space and they provide a classification of transitive dynamical systems in terms of equicontinuity pairs.In particular,under the condition that X is a Hausdorff uniform space,they give a dichotomy theorem between Hausdorff sensitivity and Hausdorff equicontinuity for G-systems admitting one transitive point.

关 键 词：Hausdorff sensitivity Hausdorff equicontinuity Topological equicontinuity Even continuity 

分 类 号：O19[理学—数学]