Description du sujet de thèse

Mixing of the geodesic flow in infinite volume

The chaotic character of certain dynamical systems makes it practically impossible to study individually their trajectories: those systems are sensible to initial conditons. Arbitrary small perturbations of the initial position lead to dramatic differences in the long term behaviour. On such example is the doubling of angles on the circle.

Another example that has been widely studied is the geodesic flow on finite area hyperbolic surfaces. When the area is infinite, but the surface has a compact quotient - as the cyclic covering of a compact surface -, the asymptotic properties of the geodesic flow is also described.

However, in infinite area but no compact quotient, much less is known: that is the tpic of this PhD. Some possibilities to approach this problem comes from work by Boulanger on orbital counting functions and the heat kernel, or from the representation theory of SL(2,R), or from techniques developped for studying the Brownian motion in this setting.

Contexte de travail

The PhD will take place at IMJ-PRG and will be co-supervised by a team consisting of Adrien Boulanger (Marseille), Gilles Courtois, and Antonin Guilloux (IMJ-PRG). The recruited individual will be based at IMJ-PRG, an environment conducive to an enriching PhD experience, with numerous internationally renowned interlocutors, an active scientific community, and attractive facilities (missions, IT equipment).