Séminaire de Géométrie, Groupes et Dynamique

Abror Pirnapasov: "Reeb orbits that force topological entropy"

435 (UMPA)




A transverse link in a contact 3-manifold forces topological entropy if every Reeb flow is possessing this link as a set of periodic orbits has positive topological entropy. 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 work with Marcelo Alves, Umberto Hryniewicz, Matthias Meiwes, and Pedro Salomão.