Classification of perturbations of the hydrogen atom by small static electric and magnetic fields

We consider perturbations of the hydrogen atom by sufficiently small homogeneous static electric and magnetic fields of all possible mutual orientations. Normalizing with regard to the Keplerian symmetry, we uncover resonances and conjecture that the parameter space of this family of dynamical systems is stratified into zones centred on the resonances. The 1 : 1 resonance corresponds to the orthogonal field limit, studied earlier by Cushman & Sadovskií (Cushman & Sadovskií 2000 Physica 142, 166-196). We describe the structure of the 1 : 1 zone, where the system may have monodromy of different kinds, and consider briefly the 1 : 2 zone.