Symbolic dynamics for three-dimensional flows with positive topological entropy

Source abstract

We construct symbolic dynamics on sets of full measure (with respect to an ergodic measure of positive entropy) for C^{1+\epsilon} flows on closed smooth three-dimensional manifolds. One consequence is that the geodesic flow on the unit tangent bundle of a closed C^\infty surface has at least const \times e^{hT}/T simple closed orbits of period less than T , whenever the topological entropy h is positive—and without further assumptions on the curvature.