Growth estimates and diameter bounds for linear algebraic groups
By Harald Helfgott
By Kasra Rafi
Appears in collection : Teichmüller Space, Polygonal Billiard, Interval Exchanges / Espace de Teichmüller. Billards polygonaux, échanges d'intervalles
The behaviour of infinite translation surfaces is, in many regards, very different from the finite case. For example, the geodesic flow is often not recurrent or is not even defined for infinite time in a generic direction. However, we show that if one focuses on a class of infinite translation surfaces that exclude the obvious counter-examples, one can adapted the proof of Kerckhoff, Masur, and Smillie and show that the geodesic flow is uniquely ergodic in almost every direction. We call this class of surface essentially finite. (joint work with Anja Randecker).