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Realisation of measured dynamics as uniquely ergodic minimal homeomorphisms on manifolds

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 نشر من قبل Frederic Le Roux
 تاريخ النشر 2008
  مجال البحث
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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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