Existence of Birkhoff sections for Kupka-Smale Reeb flows of closed
contact 3-manifolds
Existence of Birkhoff sections for Kupka-Smale Reeb flows of closed
contact 3-manifolds
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 …