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Generalized specification property and distributionally scrambled sets. (English) Zbl 1443.37010

Summary: Suppose the dynamical system \((X, f)\) has generalized specification property. In this paper, we research the existence of the (invariant) Mycielski distributionally scrambled sets for dynamical system \((X, f)\). Moreover, some properties about measure center are discussed and a dichotomy theorem is proved.

MSC:

37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
37B25 Stability of topological dynamical systems
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