Multifractal analysis of homological growth rates for hyperbolic surfaces
Dynamical Systems
2025-02-12 v2
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 Poincar\'e 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.
Keywords
Cite
@article{arxiv.2204.08907,
title = {Multifractal analysis of homological growth rates for hyperbolic surfaces},
author = {Johannes Jaerisch and Hiroki Takahasi},
journal= {arXiv preprint arXiv:2204.08907},
year = {2025}
}
Comments
32 pages, 4 figures. former title: Multifractal analysis and large deviations of homological growth rates for hyperbolic surfaces