From Poincaré Maps to Lagrangian Descriptors: The Case of the Valley Ridge Inflection Point Potential

In this paper we compare the method of Lagrangian descriptors with classical Poincare maps for revealing phase space structure two degree-of-freedom Hamiltonian systems. The comparison is carried out by considering dynamics a system having valley ridge inflection point (VRI) potential energy surface. VRI surfaces have four critical points: high saddle and lower separating wells. between points that where surface geometry changes from to ridge. region saddles forms reaction channel dynamical issue interest how trajectories cross saddle, evolve towards select particular well enter. are compared their ability determine structures govern process.