Séminaires : Séminaire de Logique Lyon-Paris

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Responsables :O. Finkel, A. Khélif, S. Rideau, T. Tsankov, A. Vignati
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Orateur(s) Matthew Foreman - University of California - Irvine,
Titre Global Structure Theorems for the space of measure preserving transformations
Date02/07/2018
Horaire15:10 à 16:10
Diffusion
RésumeIn 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.
SalleZoom ID: 824 8220 9628; s'inscrire à la liste ou contacter silvain.rideau@imj-prg.fr pour le mot de passe.
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