Collapse of the Zeeman structure of the hydrogen atom in an external electric field

We analyze the transition from a Zeeman to a Stark structure of a weakly split Rydberg {ital n} multiplet of the H atom in parallel magnetic and electric fields. The use of classical mechanics, topology, and group theory provides a detailed description of the modifications of dynamics due to the variation of the electric field. We focus on the point where the collapse of the Zeeman structure occurs, give the sequence of classical bifurcations responsible for the transition between different dynamic regimes, and compare it to the quantum energy-level structure. {copyright} {ital 1996 The American Physical Society.}