Real-analytic realization of Uniform Circular Systems and some applications

Recently Matthew Foreman and Benjamin Weiss showed in a series of papers that smooth ergodic diffeomorphisms certain compact manifolds are unclassifiable up to measure-isomorphism. In this paper we show the uniform circular systems used work Foreman—Weiss admit real-analytic realizations on two-dimensional torus. As consequence obtain same anti-classification result for another application existence an uncountable family pairwise non-Kakutani equivalent