Conventionally stable manifold

Up to moderately high energy ( 179%) of the activation barrier for reactant product in the Are isomerization reaction, the fates of most trajectories can be predicted more accurately by Eq. (11) as the order of perturbation calculation increases, except just in the vicinity of the (approximate) stable invariant manifolds (e.g., see Eig. 5), and that the transmission coefficient K observed in the configurational space can also be reproduced by the dynamical propensity rule without any elaborate trajectory calculation (see Eig. 6). Our findings indicate that almost all observed deviations from unity of the conventional transmission coefficient k may be due to the choice of the reaction coordinate whenever the k arises from the recrossings, and most transitions in chemical... 

The conventional theory of reaction processes relies on equilibrium statistical physics where the equi-energy surface is uniformly covered by orbits as shown in Fig. 34. To the contrary, the phase space in multidimensional chaos has various invariant structures, and orbits wander around these structures as shown in Fig. 35. In these processes, those degrees of freedom that constitute the movement along stable or unstable manifolds vary from NHIM to NHIM. Their variance reveals how reaction coordinates change during successive processes in reaction dynamics. 

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