JOURNAL ARTICLE

SOME FRACTALS RELATED TO PARTIAL MAXIMAL DIGITS IN LÜROTH EXPANSION.

  • Published In: Fractals, 2024, v. 32, n. 5. P. 1 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: DENG, JIANG; MA, JIHUA; SONG, KUNKUN; XIE, ZHONGQUAN 3 of 3

Abstract

Let [ d 1 (x) , d 2 (x) , ... , d n (x) , ... ] be the Lüroth expansion of x ∈ (0 , 1 ] , and let L n (x) = max { d 1 (x) , ... , d n (x) }. It is shown that for any α ≥ 0 , the level set x ∈ (0 , 1 ] : lim n → ∞ L n (x) log log n n = α has Hausdorff dimension one. Certain sets of points for which the sequence { L n (x) } n ≥ 1 grows more rapidly are also investigated. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Fractals. 2024/06, Vol. 32, Issue 5, p1
  • Document Type:Article
  • Subject Area:Mathematics
  • Publication Date:2024
  • ISSN:0218-348X
  • DOI:10.1142/S0218348X24500786
  • Accession Number:178720324
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