Apparaît dans la collection : 1923-2023, Centenaire de René Thom

Every non degenerate Reeb vector field on a closed 3-manifold is carried by a broken book decomposition. A broken book provides a system of transverses surfaces to the flow that allow to code the dynamics, allowing to prove several generic properties of Reeb vector fields. After explaining these results, I will present recent work on the existence of homoclinic orbits for Reeb vector fields. This is work in collaboration with V. Colin, P. Dehornoy and U. Hryniewicz.