MULTIFRACTAL ANALYSIS OF THE CONVERGENCE EXPONENT IN CONTINUED FRACTIONS

doi:10.1007/s10473-021-0607-1

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (6): 1896-1910.doi: 10.1007/s10473-021-0607-1

MULTIFRACTAL ANALYSIS OF THE CONVERGENCE EXPONENT IN CONTINUED FRACTIONS

房路路¹, 马际华², 宋昆昆³, 吴敏⁴

1. School of Science, Nanjing University of Science and Technology, Nanjing 210094, China;
2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;
3. Key Laboratory of Computing and Stochastic Mathematics(Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China;
4. School of Mathematics, South China University of Technology, Guangzhou 510640, China

收稿日期:2021-03-16 修回日期:2021-09-02 出版日期:2021-12-25 发布日期:2021-12-27
通讯作者: Kunkun SONG,E-mail:songkunkun@hunnu.edu.cn E-mail:songkunkun@hunnu.edu.cn
作者简介:Lulu FANG,E-mail:fanglulu1230@gmail.com;Jihua MA,E-mail:jhma@whu.edu.cn;Min WU,E-mail:wumin@scut.edu.cn
基金资助:
This research was supported by National Natural Science Foundation of China (11771153, 11801591, 11971195, 12171107), Guangdong Natural Science Foundation (2018B0303110005), Guangdong Basic and Applied Basic Research Foundation (2021A1515010056). Kunkun Song would like to thank China Scholarship Council (CSC) for financial support (201806270091).

MULTIFRACTAL ANALYSIS OF THE CONVERGENCE EXPONENT IN CONTINUED FRACTIONS

Lulu FANG¹, Jihua MA², Kunkun SONG³, Min WU⁴

1. School of Science, Nanjing University of Science and Technology, Nanjing 210094, China;
2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;
3. Key Laboratory of Computing and Stochastic Mathematics(Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China;
4. School of Mathematics, South China University of Technology, Guangzhou 510640, China

Received:2021-03-16 Revised:2021-09-02 Online:2021-12-25 Published:2021-12-27
Supported by:
This research was supported by National Natural Science Foundation of China (11771153, 11801591, 11971195, 12171107), Guangdong Natural Science Foundation (2018B0303110005), Guangdong Basic and Applied Basic Research Foundation (2021A1515010056). Kunkun Song would like to thank China Scholarship Council (CSC) for financial support (201806270091).

摘要/Abstract

摘要： Let $x \in (0,1)$ be a real number with continued fraction expansion $[a_1(x),a_2(x),$ $ a_3(x),\cdots]$. This paper is concerned with the multifractal spectrum of the convergence exponent of $\{a_n(x)\}_{n \geq 1}$ defined by \[\tau(x):=\inf\bigg\{s \geq 0:\sum_{n \geq 1} a^{-s}_n(x)<\infty\bigg\}. \]

关键词: multifractal analysis, convergence exponent, continued fractions

Abstract: Let $x \in (0,1)$ be a real number with continued fraction expansion $[a_1(x),a_2(x),$ $ a_3(x),\cdots]$. This paper is concerned with the multifractal spectrum of the convergence exponent of $\{a_n(x)\}_{n \geq 1}$ defined by \[\tau(x):=\inf\bigg\{s \geq 0:\sum_{n \geq 1} a^{-s}_n(x)<\infty\bigg\}. \]

Key words: multifractal analysis, convergence exponent, continued fractions

中图分类号:

11K50

房路路, 马际华, 宋昆昆, 吴敏. MULTIFRACTAL ANALYSIS OF THE CONVERGENCE EXPONENT IN CONTINUED FRACTIONS[J]. 数学物理学报(英文版), 2021, 41(6): 1896-1910.

Lulu FANG, Jihua MA, Kunkun SONG, Min WU. MULTIFRACTAL ANALYSIS OF THE CONVERGENCE EXPONENT IN CONTINUED FRACTIONS[J]. Acta mathematica scientia,Series B, 2021, 41(6): 1896-1910.

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MULTIFRACTAL ANALYSIS OF THE CONVERGENCE EXPONENT IN CONTINUED FRACTIONS

MULTIFRACTAL ANALYSIS OF THE CONVERGENCE EXPONENT IN CONTINUED FRACTIONS

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