The role of normally hyperbolic invariant manifolds (NHIMS) in the context of the phase space setting for chemical reaction dynamics

In this paper we give an introduction to the notion of a normally hyperbolic invariant manifold (NHIM) and its role in chemical rection dynamics. We do this by considering simple examples for one, two, and three degree-of-freedom systems where explict calculations can be carried out for all of the relevant geometrical stuctures and their properties can be explicitly understood. We specifically emphasise the notion of a NHIM as a ''phase space concept''. In particular, we make the observation that the (phase space) NHIM plays the role of ''carrying'' the (configuration space) properties of a saddle point of the potential energy surface into phase space.

We also consider an explicit example of a 2 degree-of-freedom system where a ''global'' dividing surface can be constructed using two index one saddles and one index two saddle. Such a dividing surface has arisen in several recent applications and, therefore, such a construction may be of wider interest.