Symbolic dynamics for three dimensional flows with positive topological entropy

Abstract

We construct symbolic dynamics on sets of full measure (w.r.t. an ergodic measure of positive entropy) for $C^{1+\epsilon }$ flows on compact smooth three-dimensional manifolds. One consequence is that the geodesic flow on the unit tangent bundle of a compact $C^{\infty }$ 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.

50 pages, to appear in J. Eur. Math. Soc

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