Classification of perturbations of the hydrogen atom by small static electric and magnetic fields Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Proc. R. Soc. A) Issue Volume 463, Number 2083 / July 08, 2007 Pages 1771-1790 DOI 10.1098/rspa.2007.1843 http://www.journals.royalsoc.ac.uk/content/g44318v573v04571 Authors K. Efstathiou Instituut voor Wiskunde en Informatica, Rijksuniversiteit Groningen, Groningen 9747 AC, The Netherlands D.A. Sadovskií & B.I. Zhilinskií UMR du CNRS 8101, Université du Littoral, 59140 Dunkerque, France Abstract: 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. Keywords: perturbed Kepler system, singular reduction, energy-momentum map, monodromy