A global structure theorem for measure preserving systems

Jeudi 14 juin 2018 14:00-15:00 - Matthew Foreman - UCI (University of California, Irvine)

Résumé : We define two classes of symbolic systems, the odometer based and the circular systems. The odometer based systems are presentations of ergodic measure preserving transformations that have odometer factors. The circular systems are symbolic presentations of Anosov-Katok diffeomorphisms.
The main result is that these two classes are isomorphic by a functor that preserves the factor structure, including compact and weakly mixing factors. We derive two consequences :

  • for every Choquet simplex K there is an ergodic measure preserving diffeomorphism T of the 2-torus with K affinely homeomorphic to the T-invariant measures.
  • there are ergodic measure-distal (generalized discrete spectrum) diffeomorphims of the 2-torus with arbitrarily large countable ordinal height, in particular with height 3.

Lieu : IMO, salle 2L8

A global structure theorem for measure preserving systems  Version PDF