{"id":"openai-math/Positive-Metric-Entropy-for-the-Standard-Map-at-Large-Parameters","pdf":"https://github.com/openai/math/blob/main/preprints/Positive-Metric-Entropy-for-the-Standard-Map-at-Large-Parameters-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Positive-Metric-Entropy-for-the-Standard-Map-at-Large-Parameters-September-23-2026","tags":["dynamical-systems","ergodic-theory","hamiltonian-systems"],"score":0,"title":"Positive Metric Entropy for the Standard Map at Large Parameters","domain":"Dynamical systems and ergodic theory","family":"146","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DS","summary":"We prove that the standard sine map of the two-dimensional torus has positive metric entropy with respect to normalized area for every sufficiently large positive parameter. This gives a full parameter tail, and hence answers Sinai's positive-parameter-measure conjecture affirmatively.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Positive metric entropy for the standard map"}