English

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