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Hausdorff Dimension Of The Limsup And Liminf Sets In Pierce Expansions

Author

Listed:
  • CAI LONG

    (School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, P. R. China)

  • YONGSHUN LIANG

    (School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, P. R. China)

  • LIUHUI LU

    (School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, P. R. China)

Abstract

In this paper, we determine the Hausdorff dimension of the limsup and liminf sets where the Pierce expansion digits grow at a rate no slower than any positive function defined on the natural numbers. Additionally, we provide similar analyses concerning the gaps and ratios between consecutive digits.

Suggested Citation

  • Cai Long & Yongshun Liang & Liuhui Lu, 2025. "Hausdorff Dimension Of The Limsup And Liminf Sets In Pierce Expansions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-10.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:05:n:s0218348x2550029x
    DOI: 10.1142/S0218348X2550029X
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