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arXiv · 2102.04904

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

R. Crossley·M. Agaoglou·M. Katsanikas·S. Wiggins
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Abstract

In this paper we compare the method of Lagrangian descriptors with the classical method of Poincare 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 two degree-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 Poincare maps are compared for their ability to determine the phase space structures that govern this dynamical process.

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R. Crossley, M. Agaoglou, M. Katsanikas, S. Wiggins. 2021-02-09. From Poincare Maps to Lagrangian Descriptors: The Case of the Valley Ridge Inflection Point Potential. https://doi.org/10.1134/s1560354721020040

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