双曲面同调增长率的多分形分析

Pub Date : 2024-09-18 DOI:10.1017/etds.2024.62

JOHANNES JAERISCH, HIROKI TAKAHASI

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引用次数: 0

摘要

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。

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Multifractal analysis of homological growth rates for hyperbolic surfaces

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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