MULTIFRACTAL ANALYSIS OF EXCEPTIONAL SETS ASSOCIATED WITH THE LAW OF THE ITERATED LOGARITHM OF PIERCE EXPANSIONS

Cai Long (), Liuhui Lu () and Yongshun Liang
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Cai Long: 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
Yongshun Liang: School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, P. R. China

FRACTALS (fractals), 2025, vol. 33, issue 07, 1-11

Abstract: Based on Shallit’s limit theorems of Pierce expansions, we introduce a novel method for computing the Hausdorff dimension of certain sets arising in Pierce expansions. We derive an explicit formula and apply it to determine the Hausdorff dimension of exceptional sets associated with the law of the iterated logarithm of Pierce expansions. Our results complement the recent work of Ahn (2024) on the Hausdorff dimension of sets related to the law of large numbers and the central limit theorem of Pierce expansions.

Keywords: Hausdorff Dimension; Pierce Expansion; Law of the Iterated Logarithm; Exceptional Set (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25500677

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