Transition state theory with quasi-periodic forcing

In this paper, we describe and implement an efficient and accurate method to compute transition states in quasi-periodically forced systems as well as their stable and unstable manifolds. We implement the method for a system that has been used in the literature several times (see e.g. Craven et al. [20]). We note that the calculations based on the method are performed in the natural coordinate systems used by chemists so that it should be easy to compare our results with experiments. The method is backed up by rigorous theorems which provide useful error bounds. It allows us to continue the transition state (and its stable/unstable manifolds) and we can increase the parameters arbitrarily close to breakdown. This raise new questions both in the mathematics of normally hyperbolic manifolds and in transition state theory.