{"id":"openai-math/Ergodicity-of-triangular-billiards-with-an-irrational-angle","pdf":"https://github.com/openai/math/blob/main/preprints/Ergodicity-of-triangular-billiards-with-an-irrational-angle-September-25-2026/Ergodicity-of-triangular-billiards-with-an-irrational-angle-September-25-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/Ergodicity-of-triangular-billiards-with-an-irrational-angle-September-25-2026","tags":["dynamical-systems","billiards","ergodic-theory"],"score":0,"title":"Ergodicity of triangular billiards with an irrational angle","domain":"Dynamical systems and ergodic theory","family":"150","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DS","summary":"We prove that the unit-speed billiard flow in every nondegenerate Euclidean triangle with at least one angle irrational relative to π is ergodic for normalized area times uniform angular measure. No genericity or Diophantine condition is required. The flow is considered outside the null set of trajectories that hit a vertex.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"Weak mixing of triangular billiards with an irrational angle"}