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Metric properties and exceptional sets of β-expansions over formal Laurent series

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Abstract.

This paper is concerned with the metric properties of β-expansions over the field of formal Laurent series. We will see that there are essential differences between β-expansions of the formal Laurent series case and the classical real case. Also the Hausdorff dimensions of some exceptional sets, with respect to the Haar measure, are determined.

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Authors and Affiliations

  1. Wuhan University, Wuhan, P.R. China

    Bing Li & Jian Xu

  2. Huazhong University of Science and Technology, Wuhan, P.R. China

    Jun Wu

Authors
  1. Bing Li
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  2. Jun Wu
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  3. Jian Xu
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Additional information

Authors’ addresses: Bing Li and Jian Xu, School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, P.R. China; Jun Wu, Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P.R. China

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Li, B., Wu, J. & Xu, J. Metric properties and exceptional sets of β-expansions over formal Laurent series. Monatsh Math 155, 145–160 (2008). https://doi.org/10.1007/s00605-008-0531-7

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  • DOI: https://doi.org/10.1007/s00605-008-0531-7

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