2014/10/31 by Marcelo R. R. Alves · 1 citation
Mathematics · #math.DS #math.SG #msc:37J05 #msc:53D42
paper · pdf · doi:10.2140/gt.2016.20.3519
published as Geom. Topol. 20 (2016) 3519-3569 · 42 pages, 2 figures. Exposition improved. Comments are welcome!
arxiv created 2015/08/18 · arxiv updated 2017/01/04
We establish a relation between the growth of the cylindrical contact homology of a contact manifold and the topological entropy of Reeb flows on this manifold. We show that if a contact manifold (M,ξ) admits a hypertight contact form λ0 for which the cylindrical contact homology has exponential homotopical growth rate, then the Reeb flow of every contact form on (M,ξ) has positive topological entropy. Using this result, we provide numerous new examples of contact 3-manifolds on which every Reeb flow has positive topological entropy.