Topological Ergodic Shadowing and Chaos on Uniform Spaces.

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. [ABSTRACT FROM AUTHOR]