Reeb orbits that force topological entropy

Reeb orbits that force topological entropy - Abror Pirnapasov

Abror Pirnapasov
Ruhr-Universität Bochum
June 5, 2020
A transverse link in a contact 3-manifold forces topological entropy if every Reeb flow possessing this link as a set of periodic orbits has positive topological entropy. We will explain how cylindrical contact homology on the complement of transverse links can be used to show that certain transverse links force topological entropy. As an application, we show that on every closed contact 3-manifold exists transverse knots that force topological entropy. We also generalize to the category of Reeb flows a beautiful result due to Denvir and Mackay, which says that if a Riemannian metric on the two-dimensional torus has a contractible closed geodesic then its geodesic flow has positive topological entropy. All this is joint works with Marcelo R.R. Alves, Umberto L. Hryniewicz and Pedro A.S. Salomão