{"paper":{"title":"On exotic rationally integrable planar dual billiards I. Complex geometry and type of dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DS","authors_text":"Alexey Glutsyuk","submitted_at":"2026-05-23T07:10:21Z","abstract_excerpt":"A planar dual billiard is a planar curve $\\gamma$ equipped with a family $(\\sigma_P)|_{P\\in\\gamma}$ of projective involutions of the projective lines $L_P$ tangent to $\\gamma$ at $P$ that fix $P$. A dual billiard is called rationally integrable, if there exists a rational function $R(x,y)$ of two variables (called first integral) whose restriction to each tangent line $L_P$ is $\\sigma_P$-invariant. In the previous author's paper it was shown that rationally integrable dual billiards exist only on conics punctured at $k$ points, $0\\leq k\\leq 4$. Their classification given there includes standar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24434","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.24434/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}