{"paper":{"title":"Limit Theorems for Horocycle Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","math.RT"],"primary_cat":"math.DS","authors_text":"Alexander Bufetov, Giovanni Forni","submitted_at":"2011-04-22T20:10:38Z","abstract_excerpt":"The main results of this paper are limit theorems for horocycle flows on compact surfaces of constant negative curvature. One of the main objects of the paper is a special family of horocycle-invariant finitely-additive Hoelder measures on rectifiable arcs. An asymptotic formula for ergodic integrals for horocycle flows is obtained in terms of the finitely-additive measures, and limit theorems follow as a corollary of the asymptotic formula. The objects and results of this paper are similar to those in [15], [16], [4] and [5] for translation flows on flat surfaces. The arguments are based on t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4502","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"}