A multifractal analysis for cuspidal windings on hyperbolic surfaces
Dynamical Systems
2018-04-19 v2 Number Theory
Abstract
In this paper we investigate the multifractal decomposition of the limit set of a finitely generated, free Fuchsian group with respect to the mean cusp winding number. We will completely determine its multifractal spectrum by means of a certain free energy function and show that the Hausdorff dimension of sets consisting of limit points with the same scaling exponent coincides with the Legendre transform of this free energy function. As a by-product we generalise previously obtained results on the multifractal formalism for infinite iterated function systems to the setting of infinite graph directed Markov systems.
Keywords
Cite
@article{arxiv.1610.05827,
title = {A multifractal analysis for cuspidal windings on hyperbolic surfaces},
author = {Johannes Jaerisch and Marc Kesseböhmer and Sara Munday},
journal= {arXiv preprint arXiv:1610.05827},
year = {2018}
}