10 oct 2016 -- 15:00
Aula B, Dip.Matematica, Università "La Sapienza", Roma
Abstract.
In this course, we aim to explain some classical results relating the dynamics of the geodesic flow of a negatively curved manifold X (ergodicity, finiteness of the Bowen-Margulis measure etc) and the asymptotic geometry of its universal covering (Hausdorff measure of the limit set of its fundamental group, the behaviour of its Poincaré series, the number of closed geodesics etc). We will try to be self-contained, and give all necessary prerequisites in the first introductory lectures (hyperbolic and negatively curved geometry, Busemann functions, limit set, description of the geodesic flow, Poincaré series and critical exponents and so on). A more detailed description of the course, together with the schedule, is available at http://www1.mat.uniroma1.it/ricerca/dottorato/corsi_2016/peigne.pdf