Transition state theory normally hyperbolic invariant manifolds

This very simple Hamiltonian is at the basis of the whole TS approach. It generalizes easily into many dimension (Section IV), is a good basis for perturbation theory [4], and is also the basis for numerical schemes, classical and semiclassical. The inclusion of angular momentum implies that some ingredients must be added (see Section V). Let us thus describe how this very simple, linear Hamiltonian supports normally hyperbolic invariant manifolds (NHIMs see Section IV for a proper discussion) separatrices and a transition state. 

In statistical reaction rate theory, the concept of transition state plays a key role. Transition states are supposed to be the boundaries between reactants and products. However, the precise formulation of the transition state as a dividing surface is only possible when we consider transition states in phase space. This is the place where the concepts of normally hyperbolic invariant manifolds (NHIMs) and their stable and unstable manifolds come into play. 

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