Equicontinuity and Sensitivity of Group Actions* |
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Authors: | Shaoting XIE Jiandong YIN |
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Affiliation: | Department of Mathematics, Nanchang University, Nanchang 330031, China. |
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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. |
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Keywords: | Hausdorff sensitivity Hausdorff equicontinuity Topological equicontinuity Even continuity |
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