{"paper":{"title":"Lagrangian Relations and Linear Point Billiards","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Andreas Knauf, Jacques F\\'ejoz, Richard Montgomery","submitted_at":"2016-06-04T22:04:05Z","abstract_excerpt":"Motivated by the high-energy limit of the $N$-body problem we construct non-deterministic billiard process. The billiard table is the complement of a finite collection of linear subspaces within a Euclidean vector space. A trajectory is a constant speed polygonal curve with vertices on the subspaces and change of direction upon hitting a subspace governed by `conservation of momentum' (mirror reflection). The itinerary of a trajectory is the list of subspaces it hits, in order. Two basic questions are: (A) Are itineraries finite? (B) What is the structure of the space of all trajectories havin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01420","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"}