Dynamics of reactions with two channels

The dynamics of a reaction is often mediated by a Transition State near a saddle point of a potential energy surface. Associated with the saddle point are invariant manifolds that guide the system from reactants to products. These structures are well understood in the case of individual saddle points, or of several saddle points that are well separated. If the energy of the system is high enough, the extent of the invariant manifolds around each saddle point will grow, and ultimately they will merge near a saddle point of rank two. There have been various approaches to characterizing the dynamics of a reactive system near a second-order saddle point, but many details remain open. I will present a numerical investigation of the relevant invariant manifolds in a model system that allows one to track their evolution.