Equicontinuity and Sensitivity of Group Actions

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.