Foulon-Hasselblatt contact surgery and orbit growth of Reeb flows

Appears in collection : Giroux 60 - Convexity in contact and symplectic topology

This talk will focus on dynamical properties of Reeb vector fields after a Legendrian surgery. Our description of the surgery was originally conceived by Foulon and Hasselblatt as a source of Anosov Reeb flows on various 3-manifolds including hyperbolic examples. I will explain that this operation often increases the complexity of Reeb flows by studying their orbit growths. This talk is based on joint works with B. Hasselblatt and P. Foulon and with S. Tapie.