Symbolic dynamics for three-dimensional flows with positive topological entropy

Yuri Lima, Omri M. Sarig

Research output: Contribution to journalArticlepeer-review

Abstract

We construct symbolic dynamics on sets of full measure (with respect to an ergodic measure of positive entropy) for C1+epsilon flows on closed smooth three-dimensional manifolds. One consequence is that the geodesic flow on the unit tangent bundle of a closed C-infinity surface has at least const x(e(hT) / T) simple closed orbits of period less than T, whenever the topological entropy h is positive-and without further assumptions on the curvature.

Original languageEnglish
Pages (from-to)199-256
Number of pages58
JournalJournal of the European Mathematical Society
Volume21
Issue number1
DOIs
StatePublished - 1 Jan 2019

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • General Mathematics

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