Expanding maps on the circle and geodesic laminations

Abstract

In this article we consider a family of orientation preserving expanding maps on the circle. We associate to each member of this family a geodesic lamination on the disc, endowed with a transversal measure. The map on the circle induces an expanding dynamical systems on the lamination. We explore relations between the geometry of the lamination and the symbolic dynamics of the circle map. We present a list of open problems.