Appears in collection : An introduction to dynamics on surfaces and random walks / Géométrie et Dynamiques sur les surfaces
In this course we give a proof of a central result in the theory of translation surfaces known as $Masur's$ $criterion$. The aim is to introduce the audience to the subject and illustrate how one can understand ergodic properties of the geodesic flow on an individual translation surface by studying the behaviour of its $SL(2,\mathbb{R})$-orbit on moduli space. The course is divided in 4 parts. Exercise sessions (TP) are also planned.
By Sébastien Labbé
By Bernat Espigule
