{"id":"openai-math/A-C1-Counterexample-to-the-Entropy-Conjecture","pdf":"https://github.com/openai/math/blob/main/preprints/A-C1-Counterexample-to-the-Entropy-Conjecture-September-25-2026/article.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-C1-Counterexample-to-the-Entropy-Conjecture-September-25-2026","tags":["dynamical-systems","topological-entropy","smooth-maps"],"score":0,"title":"A C^1 Counterexample to the Entropy Conjecture","domain":"Dynamical systems and ergodic theory","family":"151","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DS","summary":"We disprove the general C 1 self-map formulation of Shub's entropy conjecture. We construct a noninvertible C 1 self-map of a compact smooth manifold without boundary whose topological entropy is zero, while its action on second real homology has eigenvalue 2. Thus the topological entropy is strictly smaller than the logarithm of the homological spectral radius.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"A C 1 counterexample to the entropy conjecture"}