Realisation of measured dynamics as uniquely ergodic minimal homeomorphisms on manifolds
Dynamical Systems
2008-07-22 v1
Abstract
We prove that the family of measured dynamical systems which can be realised as uniquely ergodic minimal homeomorphisms on a given manifold (of dimension at least two) is stable under measured extension. As a corollary, any ergodic system with an irrational eigenvalue is isomorphic to a uniquely ergodic minimal homeomorphism on the two-torus. The proof uses the following improvement of Weiss relative version of Jewett-Krieger theorem: any extension between two ergodic systems is isomorphic to a skew-product on Cantor sets.
Keywords
Cite
@article{arxiv.0807.3260,
title = {Realisation of measured dynamics as uniquely ergodic minimal homeomorphisms on manifolds},
author = {François Béguin and Sylvain Crovisier and Frédéric Le Roux},
journal= {arXiv preprint arXiv:0807.3260},
year = {2008}
}