Z^d-actions with prescribed topological and ergodic properties

We extend constructions of Hahn-Katznelson and Pavlov to Z^d-actions on symbolic dynamical spaces with prescribed topological and ergodic properties. More specifically, we describe a method to build Z^d-actions which are (totally) minimal, (totally) strictly ergodic and have positive topological entropy.Comment: 19 pages, 1 figure, referee suggestions incorporated, to appear in Ergodic Theory and Dynamical System

Ergodic properties of equilibrium measures for smooth three dimensional flows

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.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