|Responsables :||O. Finkel, T. Ibarlucía, A. Khélif, S. Rideau, A. Vignati|
|Email des responsables :|
|Adresse :||Sophie Germain|
|Orateur(s)||Matthew Foreman - University of California - Irvine,|
|Titre||Global Structure Theorems for the space of measure preserving transformations|
|Horaire||15:10 à 16:10|
|Résume||In joint work with B. Weiss we show that there is a very large class of ergodic transformations (a “cone” under the pre-ordering 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 Lebesgue-measure 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 well-known problems such as the existence of ergodic Lebesgue measure preserving diffeomorphisms with an arbitrary compact Choquet simplices of invariant measures and the existence of measure-distal 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.