Dynamical Resistance Day

Partially hyperbolic diffeomorphism on 3-manifolds
24 de Abril | 11h00min | Christian Bonatti (Univ. Bourgogne, França)

Title: Partially hyperbolic diffeomorphism on 3-manifolds (video)

Partially hyperbolic diffeomorphisms is a structure which allowed to build the first examples of non-hyperbolic undecomposable dynamical systems, in the topological and ergodical meaning: robustly transitive, or stably ergodic. Until the last decades, there were few examples in dimension 3. Up to finite cover or iteration the examples fit into the following categories:

      - skew products of Anosov linear automorphisms of the 2-torus by diffeomorphisms of the circle
      - central deformations of Anosov linear automorphisms of the 3 torus
      - discretisations of Anosov flows

Does there exist other examples? This problem is known as "Pujals' conjecture", after a talk where Enrique Pujals presented the partially hyperbolic diffeomorphisms as being one of these examples. I will discuss this conjecture, which has recent progress in both directions.