An ergodic invertible zero-entropy transformation of a standard nonatomic probability space is not measurably conjugate to any C∞ diffeomorphism preserving a strictly positive smooth probability density on a compact finite-dimensional manifold.
An ergodic invertible zero-entropy transformation of a standard nonatomic probability space is not measurably conjugate to any C∞ diffeomorphism preserving a strictly positive smooth probability density on a compact finite-dimensional manifold.
An ergodic invertible zero-entropy transformation of a standard nonatomic probability space is not measurably conjugate to any C∞ diffeomorphism preserving a strictly positive smooth probability density on a compact finite-dimensional manifold.
If correct, shows that even zero entropy does not guarantee smooth positive-volume realization in any finite dimension.
Does zero entropy guarantee a smooth positive-volume model for an ergodic system?
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OpenAI reports a zero-entropy system without a smooth positive-volume model
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