Special session celebrating Ch. Bonatti's 60th birthday

10h30min-11h20 | Vyacheslav Grines and Olga Pochinka (IHS, Nizhny Novgorod,Russia)
Title: Classification of structural stable diffeomorphisms: a wonderful collaboration with wonderful Christian (video)

The joint creative work with Christian Bonatti lasts more than 20 years and has brought fundamental results in hyperbolic theory. The main direction of activity is related to the classification of structurally stable diffeomorphisms on manifolds of dimensions 2 and 3. The ideas of the obtained results and new projects concerning both regular and chaotic dynamics will be presented in the report.

 11h40min-12h30 | Matilde Martínez (CMAT, Uruguay)
Title: Unique ergodicity of the horocycle flow for Riemannian foliations (video)

A well-known theorem due to Furstenberg states that the horocycle flow on the unit tangent bundle of a compact hyperbolic surface is uniquely ergodic. In this talk, the setting will be a compact manifold endowed with a foliation by hyperbolic surfaces. On such an object, the "foliated horocycle flow" has similarities with the horocycle flow on a compact surface, but also has dynamical features which come from the dynamics of the foliation. I will discuss some examples which show that many factors come into play when addressing the question of unique ergodicity. Finally, I will present a theorem stating that for minimal Riemannian foliations by hyperbolic surfaces the horocycle flow is uniquely ergodic. This is joint work with F.Alcalde, F.Dal'Bo and A.Verjovsky.

13h30min-14h20min | François Béguin (Univ. Paris 13., France)
Title: A nice example of non-uniformly hyperbolic dynamical system coming from General Relativity (video)

Spatially homogeneous spacetimes are simplified models for our universe in General Relativity. The time-evolution of the geometry of these spacetimes is governed by a four-dimensional vector field. This vector field exhibits a very interesting strange attractor, which I would describe as a « bunch of infinitely many intertwined Bowen eyes attractors, with some non-uniformly hyperbolic behavior ». I will describe this system, explain what is known and believed about its dynamics, and relate it to a long standing conjecture General Relativity stating that « generic spacetimes should present a chaotically oscillating geometry close to their initial singularity ».

15h15min-16h10 | Amie Wilkinson (Chicago Univ., USA)
Title: Asymmetrical diffeomorphims and the C1 topology (video)