Symbolic description of periodic orbits for the quadratic Zeeman effect

The organization of the periodic orbits of a hydrogen atom in a uniform magnetic field is studied. It is shown that the dynamics is qualitatively different from that for weak fields and negative energies. The orbits can be mapped one-to-one onto a ternary symbolic tree, an organization which turns out to be applicable for all values of energy and field strength. The results indicate that the field-free hydrogen atom has a purely chaotic limit for positive energies.