Gluing torus families across a singularity: The lens space for the hydrogen atom in crossed fields

We demonstrate that topological information that can be extracted from periodic orbits in a near-integrable system can lead to a complete topological characterization of families of invariant 2-tori in terms of lens spaces. This approach ties in with the techniques we developed for classifying the tori in systems with more than two degrees of freedom. It therefore offers a general way to investigate families of invariant 2-tori in higher-dimensional Hamiltonian systems.