1,491 research outputs found
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 be a smooth flow with positive speed and positive topological
entropy on a compact smooth three dimensional manifold, and let be an
ergodic measure of maximal entropy. We show that either is Bernoulli,
or 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
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