Realisation of measured dynamics as uniquely ergodic minimal homeomorphisms on manifolds

Béguin, François; Crovisier, Sylvain; Roux, Frédéric Le

Realisation of measured dynamics as uniquely ergodic minimal homeomorphisms on manifolds

Authors

Béguin, François

Crovisier, Sylvain

Roux, Frédéric Le

Description

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.