Let {Tt} be a smooth flow with positive speed and positive topological
entropy on a compact smooth three dimensional manifold, and let μ be an
ergodic measure of maximal entropy. We show that either {Tt} is Bernoulli,
or {Tt} is isomorphic to the product of a Bernoulli flow and a rotational
flow. Applications are given to Reeb flows.Comment: 32 pages, 1 figure, a section on equilibrium measures for multiples
of the geometric potential has been added, to appear in Commentarii
Mathematici Helvetic