Séminaire - Juin
Le séminaire aura lieu un mercredi par mois de 14h à 15h à l'Institut Henri Poincaré à Paris. Pour télécharger l'affiche du mois: juin.pdf.
- 15/06/2022 - Etienne Bonnafoux (École Polytechnique) - salle 01
Titre:
Polynomial bound on the rate of mixing of the earthquake flow.
Resumé: The
earthquake flow is a tool in hyperbolic geometry helping in various
contexts from the Nielsen realization problem to the asymptotic
counting of simple closed geodesic.
Its ergodic properties remain as yet partially understood. We know that
it is mixing with respect to a so-called Mirzakhani measure. But its
mixing rate is unknown. In this presentation, I will explain how to
bound the rate of mixing of the earthquake flow, it could at most be
polynomial with a degree dependent on the topology of the surface. To
do so, we exhibit a family of functions pairs which support do not
intersect during a control amount of earthquaking. By controlling their
Lipschitz norms and integrals using hyperbolic geometry, we exclude
high rates of mixing.