Non-standard smooth realizations of Liouville rotations
We augment the C∞ conjugation approximation method with explicit estimates on the conjugacy map. This allows us to construct ergodic volume-preserving diffeomorphisms measure-theoretically isomorphic to any a priori given Liouville rotation on a variety of manifolds. In the special case of tori the maps can be made uniquely ergodic. © 2007 Cambridge University Press.
Ergodic Theory and Dynamical Systems
Fayad, B., Saprykina, M., & Windsor, A. (2007). Non-standard smooth realizations of Liouville rotations. Ergodic Theory and Dynamical Systems, 27 (6), 1803-1818. https://doi.org/10.1017/S0143385707000314