Phase Space Analysis of the Nonexistence of Dynamical Matching in a Stretched Caldera Potential Energy Surface

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Abstract

In this paper, we continue our studies of the two-dimensional caldera potential energy surface in a parametrized family that allows for a study of the effect of symmetry on the phase space structures that govern how trajectories enter, cross, and exit the region of the caldera. As a particular form of trajectory crossing, we are able to determine the effect of symmetry and phase space structure on dynamical matching. We show that there is a critical value of the symmetry parameter which controls the phase space structures responsible for the manner of crossing, interacting with the central region (including trapping in this region) and exiting the caldera. We provide an explanation for the existence of this critical value in terms of the behavior of the Hénon stability parameter for the associated periodic orbits.

Original languageEnglish
Article number1950057
Number of pages9
JournalInternational Journal of Bifurcation and Chaos
Volume29
Issue number4
DOIs
Publication statusPublished - 1 Apr 2019

Keywords

  • caldera potential
  • Chemical reaction dynamics
  • Hamiltonian system
  • invariant manifolds
  • periodic orbits
  • phase space transport
  • Poincaré section
  • symmetry

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