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Strictly Ergodic Models Under Face and Parallelepiped Group Actions

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Abstract

The Jewett–Krieger theorem states that each ergodic system has a strictly ergodic topological model. In this article, we show that for an ergodic system one may require more properties on its strictly ergodic model. For example, the orbit closure of points in diagonal under face transforms may be also strictly ergodic. As an application, we show the pointwise convergence of ergodic averages along cubes, which was firstly proved by Assani (J Anal Math 110:241–269, 2010).

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Authors and Affiliations

  1. Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences, Hefei, 230026, Anhui, People’s Republic of China

    Wen Huang, Song Shao & Xiangdong Ye

  2. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, Anhui, People’s Republic of China

    Wen Huang, Song Shao & Xiangdong Ye

Authors
  1. Wen Huang
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  2. Song Shao
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  3. Xiangdong Ye
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Corresponding author

Correspondence to Song Shao.

Additional information

Huang is partially supported by NNSF for Distinguished Young Schooler (11225105), and all authors are supported by NNSF of China (11371339, 11431012, 11571335) and by the Fundamental Research Funds for the Central Universities.

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Huang, W., Shao, S. & Ye, X. Strictly Ergodic Models Under Face and Parallelepiped Group Actions. Commun. Math. Stat. 5, 93–122 (2017). https://doi.org/10.1007/s40304-017-0102-0

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  • DOI: https://doi.org/10.1007/s40304-017-0102-0

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