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Topological ergodic shadowing and chaos on uniform spaces. (English) Zbl 1387.37007

Summary: This paper firstly proves that every dynamical system defined on a Hausdorff uniform space with topologically ergodic shadowing is topologically mixing, thus topologically chain mixing. Then, the following is proved: (1) every weakly mixing dynamical system defined on a second countable Baire-Hausdorff uniform space is chaotic in the sense of both Li-Yorke and Auslander-Yorke; (2) every point transitive dynamical system defined on a Hausdorff uniform space is either almost equicontinuous or sensitive.

MSC:

37A25 Ergodicity, mixing, rates of mixing
37B10 Symbolic dynamics
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