{"id":"openai-math/A-smooth-three-torus-diffeomorphism-with-simple-Lebesgue-spectrum","pdf":"https://github.com/openai/math/blob/main/preprints/A-smooth-three-torus-diffeomorphism-with-simple-Lebesgue-spectrum-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-smooth-three-torus-diffeomorphism-with-simple-Lebesgue-spectrum-September-23-2026","tags":["ergodic-theory","smooth-dynamics","koopman-operator"],"score":0,"title":"A smooth three-torus diffeomorphism with simple Lebesgue spectrum","domain":"Dynamical systems and ergodic theory","family":"144","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DS","summary":"We solve the probability-preserving form of Banach's simple Lebesgue-spectrum problem in smooth dynamics. We construct a C ∞ diffeomorphism of the three-torus that preserves standard volume and whose Koopman operator has simple Lebesgue spectrum on the entire mean-zero L 2 space.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Banach’s simple Lebesgue-spectrum problem"}