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A hierarchical ordering is demonstrated for the periodic orbits in a stronglycoupled multidimensional Hamiltonian system, namely the hydrogen atom incrossed electric and magnetic fields. It mirrors the hierarchy of brokenresonant tori and thereby allows one to characterize the periodic orbits by aset of winding numbers. With this knowledge, we construct the action variablesas functions of the frequency ratios and carry out a semiclassical torusquantization. The semiclassical energy levels thus obtained agree well withexact quantum calculations

Hydrogen atom in crossed electric and magnetic fields: Phase space topology and torus quantization via periodic orbits