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2013
Impact Factor

Rebecca Crossley

Publications:

Crossley R., Agaoglou M., Katsanikas M., Wiggins S.
From Poincaré Maps to Lagrangian Descriptors: The Case of the Valley Ridge Inflection Point Potential
2021, vol. 26, no. 2, pp.  147-164
Abstract
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.
Keywords: phase space structure, periodic orbits, stable and unstable manifolds, homoclinic and heteroclinic orbits, Poincar´e maps, Lagrangian descriptors
Citation: Crossley R., Agaoglou M., Katsanikas M., Wiggins S.,  From Poincaré Maps to Lagrangian Descriptors: The Case of the Valley Ridge Inflection Point Potential, Regular and Chaotic Dynamics, 2021, vol. 26, no. 2, pp. 147-164
DOI:10.1134/S1560354721020040

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