Analysis · Oct 6, 2026
Zero entropy does not guarantee a smooth positive-volume model
Constructs a zero-entropy ergodic invertible transformation of a standard nonatomic probability space that is not measurably conjugate to any C∞ diffeomorphism preserving a strictly positive smooth probability density on a compact finite-dimensional manifold. One example rules out every finite dimension.
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Unreleased OpenAI model
AI systems: Unreleased OpenAI model