We examine the phase space structures that govern reaction dynamics in the absence of
critical points on the potential energy surface. We show that in the vicinity of hyperbolic
invariant tori, it is possible to define phase space dividing surfaces that are analogous to the
dividing surfaces governing transition from reactants to products near a critical point of the
potential energy surface. We investigate the problem of capture of an atom by a diatomic
molecule and show that a normally hyperbolic invariant manifold exists at large atom-diatom …