{"paper":{"title":"A Central Limit Theorem for Periodic Orbits of Hyperbolic Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Richard Sharp, Stephen Cantrell","submitted_at":"2018-05-15T10:34:32Z","abstract_excerpt":"We consider a counting problem in the setting of hyperbolic dynamics. Let $\\phi_t : \\Lambda \\to \\Lambda$ be a weak mixing hyperbolic flow. We count the proportion of prime periodic orbits of $\\phi_t$, with length less than $T$, that satisfy an averaging condition related to a H\\\"older continuous function $f: \\Lambda \\to \\mathbb{R}$. We show, assuming an approximability condition on $\\phi$, that as $T \\to \\infty$, we obtain a central limit theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05692","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"}