Let ${T^t}$ be a smooth flow with positive speed and positive topological entropy on a compact smooth three dimensional manifold, and let $mu$ be an ergodic measure of maximal entropy. We show that either ${T^t}$ is Bernoulli, or ${T^t}$ is isomorphi
c to the product of a Bernoulli flow and a rotational flow. Applications are given to Reeb flows.
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.
