Nonstandard Smooth Realizations of Liouville Rotations

Details Nonstandard Smooth Realizations of Liouville Rotations Nonstandard Smooth Realizations of Liouville Rotations

2006-08-14

arxiv.org/abs/math/0608322v1

Mathematics

Dynamical Systems

Scientific paper

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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