Real-analytic realization of Uniform Circular Systems and some applications
Dynamical Systems
2020-04-02 v2
Abstract
Recently Matthew Foreman and Benjamin Weiss showed in a series of papers that smooth ergodic diffeomorphisms of a compact manifold are unclassifiable up to measure-isomorphism. In this paper we show that the uniform circular systems used in the work of Foreman-Weiss admit real-analytic realizations on the torus. As a consequence we obtain the same anti-classification result for real-analytic ergodic diffeomorphisms on the torus. In another application we show the existence of an uncountable family of pairwise non-Kakutani equivalent real-analytic diffeomorphisms on the torus.
Keywords
Cite
@article{arxiv.1705.05079,
title = {Real-analytic realization of Uniform Circular Systems and some applications},
author = {Shilpak Banerjee and Philipp Kunde},
journal= {arXiv preprint arXiv:1705.05079},
year = {2020}
}
Comments
47 pages. arXiv admin note: text overlap with arXiv:1508.00627 by other authors