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| Equicontinuity and Sensitivity of Group Actions* |
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Citation： |
Shaoting XIE,Jiandong YIN.Equicontinuity and Sensitivity of Group Actions*[J].Chinese Annals of Mathematics B,2023,44(4):501~516 |
| Page view： 1237
Net amount： 726 |
Authors： |
Shaoting XIE; Jiandong YIN |
Foundation： |
This work was supported by the National Natural Science Foundation of China (Nos. 12061043,11661054). |
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| Abstract： |
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 T3-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. |
Keywords： |
Hausdorff sensitivity, Hausdorff equicontinuity, Topological equicontinuity, Even continuity |
Classification： |
17B40, 17B50 |
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