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Weakly mixing proximal topological models for ergodic systems and applications

Volume 236 / 2017

Zhengxing Lian, Song Shao, Xiangdong Ye Fundamenta Mathematicae 236 (2017), 161-185 MSC: Primary 37B05; Secondary 37A05. DOI: 10.4064/fm76-2-2016 Published online: 26 August 2016

Abstract

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.

Authors

  • Zhengxing LianWu 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
    e-mail
  • Song ShaoWu 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
    e-mail
  • Xiangdong YeWu 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
    e-mail

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