UNIFORM DIOPHANTINE APPROXIMATION TO CANTOR SERIES EXPANSION

Yan Han and Chao Ma
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Yan Han: Faculty of Information Technology, Macau University of Science and Technology, Macau, P. R. China
Chao Ma: Faculty of Information Technology, Macau University of Science and Technology, Macau, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 07, 1-13

Abstract: In this paper, we study the uniform Diophantine approximation in the nonautonomous dynamic system generated by the Cantor series expansions, which is formulated by considering the following set: {x ∈ [0, 1) : ∀N ≫ 1,there is an integern ∈ [1,N],such thatTQnx ≤ (q 1q2⋯qN)−v̂}. It is of Hausdorff dimension (1−v̂ 1+v̂)2 for 0 ≤v̂ ≤ 1 and is countable for v̂ > 1 under the condition that limn→∞ log qn log(q1⋯qn) = 0.

Keywords: Uniform Diophantine Approximation; Hausdorff Dimension; Cantor Series Expansion (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21502066

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