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Unique Ergodicity for Zero-entropy Dynamical Systems with the Approximate Product Property

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Abstract

We show that for every topological dynamical system with the approximate product property, zero topological entropy is equivalent to unique ergodicity. Equivalence of minimality is also proved under a slightly stronger condition. Moreover, we show that unique ergodicity implies the approximate product property if the system has periodic points.

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Acknowledgements

The author would like to thank Xueting Tian, Jian Li and the anonymous referees for their helpful comments.

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Authors and Affiliations

  1. China Economics and Management Academy, Central University of Finance and Economics, Beijing, 100081, P.R. China

    Peng Sun

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  1. Peng Sun
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Correspondence to Peng Sun.

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Supported by National Natural Science Foundation of China (Grant No. 11571387) and CUFE Young Elite Teacher Project (Grant No. QYP1902)

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Sun, P. Unique Ergodicity for Zero-entropy Dynamical Systems with the Approximate Product Property. Acta. Math. Sin.-English Ser. 37, 362–376 (2021). https://doi.org/10.1007/s10114-020-9377-2

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