Multifractal analysis of homological growth rates for hyperbolic surfaces

IF 0.8 3区数学 Q2 MATHEMATICS

Ergodic Theory and Dynamical Systems Pub Date : 2024-09-18 DOI:10.1017/etds.2024.62

JOHANNES JAERISCH, HIROKI TAKAHASI

引用次数: 0

Abstract

We perform a multifractal analysis of homological growth rates of oriented geodesics on hyperbolic surfaces. Our main result provides a formula for the Hausdorff dimension of level sets of prescribed growth rates in terms of a generalized Poincaré exponent of the Fuchsian group. We employ symbolic dynamics developed by Bowen and Series, ergodic theory and thermodynamic formalism to prove the analyticity of the dimension spectrum.

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双曲面同调增长率的多分形分析

我们对双曲面上定向大地线的同调增长率进行了多分形分析。我们的主要结果提供了一个关于规定增长率的水平集的豪斯多夫维度的公式，该公式是用福氏群的广义波恩卡列指数表示的。我们采用鲍恩和系列所发展的符号动力学、遍历理论和热力学形式主义来证明维度谱的解析性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Ergodic Theory and Dynamical Systems 数学-数学

CiteScore

1.70

自引率

11.10%

发文量

113

审稿时长

6-12 weeks

期刊介绍： Ergodic Theory and Dynamical Systems focuses on a rich variety of research areas which, although diverse, employ as common themes global dynamical methods. The journal provides a focus for this important and flourishing area of mathematics and brings together many major contributions in the field. The journal acts as a forum for central problems of dynamical systems and of interactions of dynamical systems with areas such as differential geometry, number theory, operator algebras, celestial and statistical mechanics, and biology.