BIFURCATIONS OF THE COMMON LEVEL SETS OF ATOMIC HYDROGEN IN VAN DER WAALS POTENTIAL

Abstract

The classical dynamics of a hydrogen atom in a generalized van der Waals potential is investigated. In order to carry out the analytical and numerical investigations for a range of parametric values, we removed the singularity of the problem using Levi–Civita regularization and converted the problem into that of two coupled sextic anharmonic oscillators. We give a complete description of the real phase space structure of the converted system and give also an explicit periodic solution for singular common-level sets of the first integrals. All generic bifurcations of Liouville tori were determined theoretically. Numerical investigations are carried out for all generic bifurcations and we observe chaos-order-chaos transition when one of the system parameters is varied.