Symbolic dynamics for three-dimensional flows with positive topological entropy

摘要

We construct symbolic dynamics on sets of full measure (with respect to an ergodic measure of positive entropy) for C1+epsilon flows on closed smooth three-dimensional manifolds. One consequence is that the geodesic flow on the unit tangent bundle of a closed C-infinity surface has at least const x(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.