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Nonstandard Smooth Realizations of Liouville Rotations

Bassam Fayad·Maria Saprykina·Alistair Windsor
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Abstract

We augment the method of $C^\infty$ conjugation approximation with explicit estimates on the conjugacy map. This allows us to construct ergodic volume preserving diffeomorphisms measure-theoretically isomorphic to any apriori given Liouville rotation on a variety of manifolds. In the special case of tori the maps can be made uniquely ergodic.

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Bassam Fayad, Maria Saprykina, Alistair Windsor. 2006-08-14. Nonstandard Smooth Realizations of Liouville Rotations. https://arxiv.org/abs/math/0608322

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