On Hausdorff dimension and cusp excursions for Fuchsian groups
Dynamical Systems
2011-11-22 v1
Abstract
Certain subsets of limit sets of geometrically finite Fuchsian groups with parabolic elements are considered. It is known that Jarn\'{\i}k limit sets determine a "weak multifractal spectrum" of the Patterson measure in this situation. This paper will describe a natural generalisation of these sets, called strict Jarn\'{\i}k limit sets, and show how these give rise to another weak multifractal spectrum. Number-theoretical interpretations of these results in terms of continued fractions will also be given.
Keywords
Cite
@article{arxiv.1111.4945,
title = {On Hausdorff dimension and cusp excursions for Fuchsian groups},
author = {Sara Munday},
journal= {arXiv preprint arXiv:1111.4945},
year = {2011}
}