The Poincar\'e exponent and the dimensions of Kleinian limit sets
Dynamical Systems
2021-08-13 v1 Metric Geometry
Abstract
We provide a proof of the (well-known) result that the Poincar\'e exponent of a non-elementary Kleinian group is a lower bound for the upper box dimension of the limit set. Our proof only uses elementary hyperbolic and fractal geometry.
Keywords
Cite
@article{arxiv.2108.05408,
title = {The Poincar\'e exponent and the dimensions of Kleinian limit sets},
author = {Jonathan M. Fraser},
journal= {arXiv preprint arXiv:2108.05408},
year = {2021}
}
Comments
Expository, 6 pages. This article has been accepted for publication in The American Mathematical Monthly, published by Taylor & Francis