Realisation of measured dynamics as uniquely ergodic minimal homeomorphisms on manifolds

François Béguin (1) , Sylvain Crovisier (2) , Frédéric Le Roux (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 LAGA - Laboratoire Analyse, Géométrie et Applications

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.

Domaines: Systèmes dynamiques [math.DS]

François Béguin, Sylvain Crovisier, Frédéric Le Roux. Realisation of measured dynamics as uniquely ergodic minimal homeomorphisms on manifolds. 2008. ⟨hal-00302854⟩