Reeb dynamics in dimension 3 and broken book decompositions

In a joint work with Pierre Dehornoy and Ana Rechtman, we prove that on a closed 3-manifold, every nondegenerate Reeb vector field is supported by a broken book decomposition. From this property, we deduce that in dimension 3 every nondegenerate Reeb vector field has either 2 or infinitely periodic orbits and that on a closed 3-manifold that is not graphed, every nondegenerate Reeb vector field has positive topological entropy.