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Some Fractals Related To Partial Maximal Digits In Lãœroth Expansion

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jiang Deng & Jihua Ma & Kunkun Song & Zhongquan Xie, 2024. "Some Fractals Related To Partial Maximal Digits In Lãœroth Expansion," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(05), pages 1-7.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:05:n:s0218348x24500786
    DOI: 10.1142/S0218348X24500786
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