Geodesic
Weakly mixing proximal topological models for ergodic systems and applications
Zhengxing Lian 1   ; Song Shao 1   ; Xiangdong Ye 1
1 Wu Wen-Tsun Key Laboratory of Mathematics USTC, Chinese Academy of Sciences and Department of Mathematics University of Science and Technology of China Hefei, Anhui, 230026, P.R. China
Fundamenta Mathematicae, Tome 236 (2017) no. 2, pp. 161-185 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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It is shown that every non-periodic ergodic system has two topologically weakly mixing, fully supported models: one is non-minimal but has a dense set of minimal points, and the other one is proximal. Also, for a given Kakutani–Rokhlin tower with relatively prime column heights, it is demonstrated how to get a new tall Kakutani–Rokhlin tower with the same property, which can be used in Weiss’s proof of Jewett–Krieger’s theorem and in the proofs of our theorems. Applications of the results are given.
DOI : 10.4064/fm76-2-2016
Keywords: shown every non periodic ergodic system has topologically weakly mixing fully supported models non minimal has dense set minimal points other proximal given kakutani rokhlin tower relatively prime column heights demonstrated get tall kakutani rokhlin tower property which weiss proof jewett krieger theorem proofs theorems applications results given

Zhengxing Lian  1   ; Song Shao  1   ; Xiangdong Ye  1

1 Wu Wen-Tsun Key Laboratory of Mathematics USTC, Chinese Academy of Sciences and Department of Mathematics University of Science and Technology of China Hefei, Anhui, 230026, P.R. China 
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Zhengxing Lian; Song Shao; Xiangdong Ye. Weakly mixing proximal topological models for ergodic systems and applications. Fundamenta Mathematicae, Tome 236 (2017) no. 2, pp. 161-185. doi: 10.4064/fm76-2-2016

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