Symbolic dynamics for three-dimensional flows with positive topological entropy

  • Yuri Lima

    Universidade Federal do Ceará, Fortaleza, Brazil
  • Omri M. Sarig

    Weizmann Institute of Science, Rehovot, Israel
Symbolic dynamics for three-dimensional flows with positive topological entropy cover
Download PDF

A subscription is required to access this article.

Abstract

We construct symbolic dynamics on sets of full measure (with respect to an ergodic measure of positive entropy) for flows on closed smooth three-dimensional manifolds. One consequence is that the geodesic flow on the unit tangent bundle of a closed surface has at least const simple closed orbits of period less than , whenever the topological entropy is positive—and without further assumptions on the curvature.

Cite this article

Yuri Lima, Omri M. Sarig, Symbolic dynamics for three-dimensional flows with positive topological entropy. J. Eur. Math. Soc. 21 (2019), no. 1, pp. 199–256

DOI 10.4171/JEMS/834