{"paper":{"title":"Variations on a Theorem of Birman and Series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Anna Lenzhen, Juan Souto","submitted_at":"2015-12-14T15:21:33Z","abstract_excerpt":"Suppose that $\\Sigma$ is a hyperbolic surface and $f:\\mathbb R_+\\to\\mathbb R_+$ a monotonic function. We study the closure in the projective tangent bundle $PT\\Sigma$ of the set of all geodesics $\\gamma$ satisfying $I(\\gamma,\\gamma)\\leq f(\\ell_\\Sigma(\\gamma))$. For instance we prove that if $f$ is unbounded and sublinear then this set has Hausdorff dimension strictly bounded between 1 and 3."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04360","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"}