HAUSDORFF DIMENSION OF THE LIMSUP AND LIMINF SETS IN PIERCE EXPANSIONS

Cai Long (), Yongshun Liang and Liuhui Lu ()
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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

FRACTALS (fractals), 2025, vol. 33, issue 05, 1-10

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.

Keywords: Hausdorff Dimension; Pierce Expansion; Limsup Set; Liminf Set (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X2550029X

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