Modul:   MAT760  Ergodic theory and dynamical systems seminar

Partial equidistribution of Farey rays in negative curvature

Talk by Dr. Frédéric Paulin

Speaker invited by: Prof. Dr. Alexander Gorodnik

Date: 24.04.23  Time: 13.30 - 14.30  Room: ETH HG G 43

In the unit tangent bundle of a finite volume Riemannian manifold with negative curvature, a closed strong unstable leaf pushed by the geodesic flow equidistributes towards the maximal entropy measure. Fixing a family of discrete points with geometric origin (intersection with divergent orbits of the geodesic flow) on these unstable leaves, and having care of taking neither too many nor too few points (using a prescribed density), we prove that the family of points equidistributes towards a measure supported on a truncated weak stable leaf. We give arithmetic applications by varying arithmetic hyperbolic manifolds. This is a joint work with Jouni Parkkonen.