Realisation of measured dynamics as uniquely ergodic minimal homeomorphisms on manifolds

2008/07/21 by Béguin, François, Crovisier, Sylvain, Roux, Frédéric Le
#37A05 #37E30. #54H20 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.0807.3260

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.

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