JournalscmhVol. 91, No. 1pp. 65–106

Ergodic properties of equilibrium measures for smooth three dimensional flows

  • François Ledrappier

    University of Notre Dame, USA
  • Yuri Lima

    Université Paris-Sud 11, Orsay, France
  • Omri M. Sarig

    The Weizmann Institute of Science, Rehovot, Israel
Ergodic properties of equilibrium measures for smooth three dimensional flows cover

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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.

Cite this article

François Ledrappier, Yuri Lima, Omri M. Sarig, Ergodic properties of equilibrium measures for smooth three dimensional flows. Comment. Math. Helv. 91 (2016), no. 1, pp. 65–106

DOI 10.4171/CMH/378