The phase topology and bifurcation tori of the Hydrogen atom subjected to external fields

Abstract

In this paper, we performed an adapted canonical transformation, and we analysed the phase space topology and the bifurcation of Liouville tori of the Hydrogen atom subjected to three static external fields: Van der Waals potential, electric and magnetic fields. In particular, for all values of the parameters of the system under consideration, the bifurcation diagrams of the momentum mapping are constructed, bifurcations of the common level sets of the first integrals are described and the all-generic bifurcations are computed for all singular points of the bifurcation diagrams. However no author has combined these three fields and studied their behavior. Numerical investigations are performed for the integrable case by means of Poincaré surfaces of section and the phase space trajectories method, and we observed the chaos-order-chaos transition