{"paper":{"title":"Families of Periodic Orbits of the Koch Snowflake Fractal Billiard","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Michel L. Lapidus, Robert G. Niemeyer","submitted_at":"2011-05-04T05:48:23Z","abstract_excerpt":"We describe the periodic orbits of the prefractal Koch snowflake billiard (the nth inner rational polygonal approximation of the Koch snowflake billiard). In the case of the finite (prefractal) billiard table, we focus on the direction given by an initial angle of pi/3, and define 1) a compatible sequence of piecewise Fagnano orbits, 2) an eventually constant compatible sequence of orbits and 3) a compatible sequence of generalized piecewise Fagnano orbits. In the case of the infinite (fractal) billiard table, we will describe what we call stabilizing periodic orbits of the Koch snowflake frac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0737","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"}