We prove the rational egodicity of geodesic flows on divergence type surfaces of constant negative curvature, and identify their asymptotic types. 0. Introduction We discuss recurrence and transitivity properties of geodesies on hyperbolic surfaces (complete, two dimensional Riemannian manifolds with constant curvature -1). Every such surface has the unit disc as universal cover and can be viewed as H/Y where H is the unit disc equipped with the hyperbolic metric and Y is the covering group of… CONTINUE READING