{"paper":{"title":"Fractal Models for Normal Subgroups of Schottky Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Johannes Jaerisch","submitted_at":"2011-05-31T20:59:06Z","abstract_excerpt":"For a normal subgroup $N$ of the free group $\\F_d$ with at least two generators we introduce the radial limit set $\\Lr(N,\\Phi)$ of $N$ with respect to a graph directed Markov system $\\Phi$ associated to $\\F_d$. These sets are shown to provide fractal models of radial limit sets of normal subgroups of Kleinian groups of Schottky type. Our main result states that if $\\Phi$ is symmetric and linear, then we have that $\\dim_{H}(\\Lr(N,\\Phi))=\\dim_{H} \\Lr(\\F_d,\\Phi))$ if and only if the quotient group $\\F_d /N$ is amenable, where $\\dim_{H}$ denotes the Hausdorff dimension. This extends a result of Br"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0026","kind":"arxiv","version":2},"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"}