Multifractal analysis of the divergence points of Birkhoff averages for beta-transformations
Multifractal analysis of the divergence points of Birkhoff averages for beta-transformations
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Beta 变换的 Birkhoff 平均值的发散点的多重分形分析
DOI：
10.1007/s00605-016-0895-z
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发表时间：
2017
影响因子：
0.9
通讯作者：
Zhao Xiaojun
中科院分区：
文献类型：
--
作者：
Chen Yuanhong;Zhang Zhenliang;Zhao Xiaojun
This paper is aimed at a detailed study of the multifractal analysis of the so-called divergence points in the system of-expansions. More precisely, letbe the-transformation on [0, 1) for a generalandbe a continuous function. Denote byall the accumulation points of. The Hausdorff dimensions of the sets \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \{x:\textsf {A}(\psi ,x)\supset [a,b]\},\quad \{x:\textsf {A}(\psi ,x)=[a,b]\},\quad \{x:\textsf {A}(\psi ,x)\subset [a,b]\} \end{aligned}$$\end{document}i.e., the points for which the Birkhoff averages ofdo not exist but behave in a certain prescribed way, are determined completely for any continuous function.
This paper is aimed at a detailed study of the multifractal analysis of the so-called divergence points in the system of-expansions. More precisely, letbe the-transformation on [0, 1) for a generalandbe a continuous function. Denote byall the accumulation points of. The Hausdorff dimensions of the sets \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \{x:\textsf {A}(\psi ,x)\supset [a,b]\},\quad \{x:\textsf {A}(\psi ,x)=[a,b]\},\quad \{x:\textsf {A}(\psi ,x)\subset [a,b]\} \end{aligned}$$\end{document}i.e., the points for which the Birkhoff averages ofdo not exist but behave in a certain prescribed way, are determined completely for any continuous function.