{"paper":{"title":"Looking for a Billiard Table which is not a Lattice Polygon but Satisfies Veech's Dichotomy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Meital Cohen","submitted_at":"2010-11-14T11:34:01Z","abstract_excerpt":"Over the course of studying billiard dynamics, several questions were raised. One of the questions was, which surfaces satisfy the following property (which is called Veech's dichotomy): Any direction is either completely periodic or uniquely ergodic. In an important paper Veech gave a sufficient condition for this dichotomy. He showed that if the stabilizer of a translation surface is a lattice in $SL_2(\\R)$, then the surface satisfies Veech's dichotomy. Later, Smillie and Weiss proved that this condition is not necessary. They constructed a translation surface which satisfies Veech's dichoto"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3217","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"}