Ergodic properties of equilibrium measures for smooth three dimensional flows

Abstract

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 isomorphic to the product of a Bernoulli flow and a rotational flow. Applications are given to Reeb flows.

32 pages, 1 figure, a section on equilibrium measures for multiples of the geometric potential has been added, to appear in Commentarii Mathematici Helvetici

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