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

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

2010-09-02

arxiv.org/abs/1009.0468v1

Mathematics

Dynamical Systems

11 pages, 3 figures

Scientific paper

The main result of this paper is to show that if $\H$ is a normal subgroup of a Kleinian group $G$ 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 $G$. This observation extends previous results by Fern\'andez and Meli\'an for Riemann surfaces.

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