Matthaios Katsanikas

In this paper we study an asymmetric valley-ridge inflection point (VRI) potential, whose energy surface (PES) features two sequential index-1 saddles (the upper and the lower), with one saddle having higher energy than the other, and two potential wells separated by the lower index-1 saddle. We show how the depth and the flatness of our potential changes as we modify the parameter that controls the asymmetry as well as how the branching ratio (ratio of the trajectories that enter each well) is changing as we modify the same parameter and its correlation with the area of the lobes as they have been formed by the stable and unstable manifolds that have been extracted from the gradient of the LD scalar fields.

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