SOME FRACTALS RELATED TO PARTIAL MAXIMAL DIGITS IN LÃœROTH EXPANSION

Jiang Deng (), Jihua Ma (), Kunkun Song and Zhongquan Xie ()
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Jiang Deng: School of Mathematics and Statistics, Hubei University of Education, Wuhan 430205, P. R. China
Jihua Ma: ��School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, P. R. China
Kunkun Song: ��Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, P. R. China
Zhongquan Xie: ��Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, P. R. China

FRACTALS (fractals), 2024, vol. 32, issue 05, 1-7

Abstract: Let [d1(x),d2(x),…,dn(x),…] be the Lüroth expansion of x ∈ (0, 1], and let Ln(x) =max{d1(x),…,dn(x)}. It is shown that for any α ≥ 0, the level set x ∈ (0, 1] :limn→∞Ln(x)loglog n n = α has Hausdorff dimension one. Certain sets of points for which the sequence {Ln(x)}n≥1 grows more rapidly are also investigated.

Keywords: Lüroth Expansion; Maximal Digits; Hausdorff Dimension (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24500786

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