  In this paper, we revisit the concepts of the reactivity map and the
reactivity bands as an alternative to the use of perturbation theory for the
determination of the phase space geometry of chemical reactions. We introduce a
reformulated metric, called the asymptotic trajectory indicator, and an
efficient algorithm to obtain reactivity boundaries. We demonstrate that this
method has sufficient accuracy to reproduce phase space structures such as
turnstiles for a 1D model of the isomerization of ketene in an external field.
The asymptotic trajectory indicator can be applied to higher dimensional
systems coupled to Langevin baths as we demonstrate for a 3D model of the
isomerization of ketene.
