  A Reeb vector field satisfies the Kupka-Smale condition when all its closed
orbits are non-degenerate, and the stable and unstable manifolds of its
hyperbolic closed orbits intersect transversely. We show that, on a closed
3-manifold, any Reeb vector field satisfying the Kupka-Smale condition admits a
Birkhoff section. In particular, this implies that the Reeb vector field of a
$C^\infty$-generic contact form on a closed 3-manifold admits a Birkhoff
section, and that the geodesic vector field of a $C^\infty$-generic Riemannian
metric on a closed surface admits a Birkhoff section.
