{"paper":{"title":"Geometric renormalisation and Hausdorff dimension for loop-approximable geodesics escaping to infinity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bernd O. Stratmann, Kurt Falk","submitted_at":"2010-09-02T16:37:02Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0468","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}