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26 April 2024

» arxiv » 1009.0468

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Geometric renormalisation and Hausdorff dimension for loop-approximable geodesics escaping to infinity
Kurt Falk ; Bernd O. Stratmann ;
Date:	2 Sep 2010
Abstract:	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.
Source:	arXiv, 1009.0468
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