论文标题
双曲线表面同源生长速率的多重分析分析
Multifractal analysis of homological growth rates for hyperbolic surfaces
论文作者
论文摘要
我们对双曲线表面的定向大地测量学的同源生长速率进行多重分析。我们的主要结果为紫红色集团的普遍庞加莱指数而言，为豪斯多夫的高度集合提供了一个公式。我们采用鲍恩（Bowen）和系列（ergodic Theory）开发的符号动力学，千古理论和热力学形式主义，以证明维度谱的分析性。
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.
