Phase Space Analysis of the Non-Existence of Dynamical Matching in a Stretched Caldera Potential Energy Surface

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 Henon stability parameter for the associated periodic orbits.

10 pages, International Journal of Bifurcation and Chaos (in press). arXiv admin note: text overlap with arXiv:1809.06702

References in corpus (2)

• Nonstatistical dynamics on the caldera
• Phase Space Structure and Transport in a Caldera Potential Energy Surface

Cited by in corpus (8)

• Detection of Dynamical Matching in a Caldera Hamiltonian System using Lagrangian Descriptors
• The Dynamical Matching Mechanism in Phase Space for Caldera-Type Potential Energy Surfaces
• The Nature of Reactive and Non-reactive Trajectories for a Three Dimensional Caldera Potential Energy Surface
• The bifurcations of the critical points and the role of the depth in a symmetric Caldera potential energy surface
• The Influence of a Pitchfork Bifurcation of the Critical Points of a Symmetric Caldera Potential Energy Surface on Dynamical Matching
• Phase space transport in a symmetric Caldera potential with three index-1 saddles and no minima
• Bifurcation of Dividing Surfaces Constructed from Period-Doubling Bifurcations of Periodic Orbits in a Caldera Potential Energy Surface
• From Poincare Maps to Lagrangian Descriptors: The Case of the Valley Ridge Inflection Point Potential