| 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 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. |
| Salle | https://bigbluebutton.imj-prg.fr/b/sil-gwg-gge |
| Adresse | Sophie Germain |
