English

Ergodic properties of equilibrium measures for smooth three dimensional flows

Dynamical Systems 2020-04-21 v2 Differential Geometry

Abstract

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

Keywords

Cite

@article{arxiv.1504.00048,
  title  = {Ergodic properties of equilibrium measures for smooth three dimensional flows},
  author = {François Ledrappier and Yuri Lima and Omri Sarig},
  journal= {arXiv preprint arXiv:1504.00048},
  year   = {2020}
}

Comments

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

R2 v1 2026-06-22T09:07:28.759Z