Bassam Fayad, Maria Saprykina, Alistair Windsor
Nonstandard Smooth Realizations of Liouville Rotations
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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.