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This article is cited in 7 scientific papers (total in 7 papers)
Special Issue: Nonlinear Dynamics in Chemical Sciences: Part II
From Poincaré Maps to Lagrangian Descriptors:
The Case of the Valley Ridge Inflection Point Potential
Rebecca Crossley, Makrina Agaoglou, Matthaios Katsanikas, Stephen Wiggins School of Mathematics, University of Bristol,
Fry Building, Woodland Road,
BS8 1UG Bristol, United Kingdom
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, Poincaré maps, Lagrangian descriptors.
Received: 16.12.2020 Accepted: 26.01.2021
Citation:
Rebecca Crossley, Makrina Agaoglou, Matthaios Katsanikas, Stephen Wiggins, “From Poincaré Maps to Lagrangian Descriptors:
The Case of the Valley Ridge Inflection Point Potential”, Regul. Chaotic Dyn., 26:2 (2021), 147–164
Linking options:
https://www.mathnet.ru/eng/rcd1108 https://www.mathnet.ru/eng/rcd/v26/i2/p147
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Abstract page: | 114 | References: | 21 |
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