拉格朗日谱左半线极值点的维数集中

IF 0.9 3区数学 Q2 MATHEMATICS

Acta Mathematica Sinica-English Series Pub Date : 2025-05-15 DOI:10.1007/s10114-025-3683-7

Carlos Gustavo Moreira, Christian Camilo Silva Villamil

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引用次数: 0

摘要

证明了对于任意属于马尔可夫谱和Lagrange谱内闭包的η，分别以η和完全η为界的Diophantine近似最佳常数的无理数集k−1(（−∞,η]）和k−1（η）具有相同的Hausdorff维数。我们还表明，当η在光谱内部变化时，这个豪斯多夫维数是一个严格的递增函数。

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Concentration of Dimension in Extremal Points of Left-half Lines in the Lagrange Spectrum

We prove that for any η that belongs to the closure of the interior of the Markov and Lagrange spectra, the sets k⁻¹((−∞, η]) and k⁻¹(η), which are the sets of irrational numbers with best constant of Diophantine approximation bounded by η and exactly η respectively, have the same Hausdorff dimension. We also show that, as η varies in the interior of the spectra, this Hausdorff dimension is a strictly increasing function.

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来源期刊

Acta Mathematica Sinica-English Series 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

138

审稿时长

14.5 months

期刊介绍： Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.