Distributional chaos on uniform spaces. (English) Zbl 1432.37035
Summary: We introduce and study here the notion of distributional chaos on uniform spaces. We prove that if a uniformly continuous self-map of a uniform locally compact Hausdorff space has topological weak specification property then it admits a topologically distributionally scrambled set of type 3. This extends result due to A. Sklar and J. Smítal [J. Math. Anal. Appl. 241, No. 2, 181–188 (2000; Zbl 1060.37012)]. We also justify through examples necessity of the conditions in the hypothesis of the main result.
MSC:
| 37B40 | Topological entropy |
| 37B05 | Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) |
Citations:
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