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Published in:
2015 | OriginalPaper | Chapter
14. Dynamical Systems Disjoint from Any Minimal System Under Group Actions
Author : Tao Yu
Published in: Difference Equations, Discrete Dynamical Systems and Applications
Publisher: Springer International Publishing
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Abstract
When \(G=\mathbb {Z}^d\), we show that if (X, G) is disjoint from all minimal systems and transitive, then (X, G) is a weakly mixing M-system without nontrivial minimal factor. Moreover, we show that if (X, G) is weakly mixing with dense distal points and with G being Abelian, then (X, G) is disjoint from all minimal systems. These generalize some related results in the case of \(G=\mathbb {Z}\).