{"paper":{"title":"Algebraic Birkhoff conjecture for billiards on Sphere and Hyperbolic plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","nlin.SI"],"primary_cat":"math.DG","authors_text":"Andrey E. Mironov, Michael (Misha) Bialy","submitted_at":"2016-02-18T07:23:02Z","abstract_excerpt":"We consider a convex curve $\\gamma$ lying on the Sphere or Hyperbolic plane. We study the problem of existence of polynomial in velocities integrals for Birkhoff billiard inside the domain bounded by $\\gamma$. We extend the result by S. Bolotin (1992) and get new obstructions on polynomial integrability in terms of the dual curve $\\Gamma$. We follow a method which was introduced by S. Tabachnikov for Outer billiards in the plane and was applied later on in our recent paper to Birkhoff billiards with the help of a new the so called Angular billiard."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05698","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"}