A characterization of weak-mixing for minimal systems. (English) Zbl 1436.37012
The author presents a characterization of weak-mixing for minimal topological dynamical systems. More precisely, the main result of the paper states that a minimal homeomorphism \(T\) on a non-trivial compact metric space \(X\) is weak-mixing if and only if there is a dense \(\sigma\)-Cantor set \(K\) of \(X\) such that for each \(d \in \mathbb{N}\) any element in \(K^d\) is a transitive point of the map \(T \times T^2 \times \cdots \times T^d\).
Reviewer: Ngoc Thach Nguyen (Daejeon)
MSC:
| 37B05 | Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) |
| 37A25 | Ergodicity, mixing, rates of mixing |
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