Orateur(s)  Matthew Foreman  University of California  Irvine,

Titre  Global Structure Theorems for the space of measure preserving transformations 
Date  02/07/2018 
Horaire  15:10 à 16:10 

Diffusion  
Résume  In joint work with B. Weiss we show that there is a very large class of ergodic transformations (a “cone” under the preordering induced by factor maps) whose joining structure is identical to another class, the “circular systems”. The latter class is of interest because every member can be realized as a Lebesguemeasure preserving diffeomorphism of the torus T^2.
Using this theorem, we are able to conclude that the joining structure among diffeomorphisms includes that of a cone of diffeomorphisms. This solves several wellknown problems such as the existence of ergodic Lebesgue measure preserving diffeomorphisms with an arbitrary compact Choquet simplices of invariant measures and the existence of measuredistal diffeomorphisms of T^2 of height greater than 2. (In fact we give examples of arbitrary countable ordinal height.)
As a bonus result we give a class of diffeomorphisms T of the torus “Godel's diffeomorphisms” for which T being isomorphic to T^1 is independent of ZFC. 
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