Index k saddles and dividing surfaces in phase space, with applications to isomerization dynamics

Understand

In this paper we continue our studies of the phase space geometry and dynamics associated with index k saddles (k > 1) of the potential energy surface.

• Using normal form theory, we give an explicit formula for a "dividing surface" in phase space, i.e.
• a co-dimension one surface (within the energy shell) through which all trajectories that "cross" the region of the index k saddle must pass.
• With a generic non-resonance assumption, the normal form provides k (approximate) integrals that describe the saddle dynamics in a neighborhood of the index k saddle.