Published online by Cambridge University Press: 12 July 2007
We study the existence of closed characteristics on three-dimensional energy manifolds of second-order Lagrangian systems. These manifolds are always non-compact, connected and not necessarily of contact type. Using the specific geometry of these manifolds, we prove that the number of closed characteristics on a prescribed energy manifold is bounded below by its second Betti number, which is easily computable from the Lagrangian.