Symbolic dynamics for three-dimensional flows with positive topological entropy
Yuri Lima
Universidade Federal do Ceará, Fortaleza, BrazilOmri M. Sarig
Weizmann Institute of Science, Rehovot, Israel
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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