English

Geometric renormalisation and Hausdorff dimension for loop-approximable geodesics escaping to infinity

Dynamical Systems 2010-09-03 v1

Abstract

The main result of this paper is to show that if \H is a normal subgroup of a Kleinian group GG such that G/\H contains a coset which is represented by some loxodromic element, then the Hausdorff dimension of the transient limit set of \H coincides with the Hausdorff dimension of the limit set of GG. This observation extends previous results by Fern\'andez and Meli\'an for Riemann surfaces.

Keywords

Cite

@article{arxiv.1009.0468,
  title  = {Geometric renormalisation and Hausdorff dimension for loop-approximable geodesics escaping to infinity},
  author = {Kurt Falk and Bernd O. Stratmann},
  journal= {arXiv preprint arXiv:1009.0468},
  year   = {2010}
}

Comments

11 pages, 3 figures

R2 v1 2026-06-21T16:08:41.129Z