SYMBOLIC DYNAMICS FOR HYDROGEN IN A MAGNETIC-FIELD

We discuss symbolic dynamics for the Hamiltonian describing the classi cal motion of hydrogen in a uniform magnetic field with zero angular m omentum. For a scaled energy above a critical value epsilon(c), the Ha miltonian has a Canter set repellor described by a three-lettered symb olic alphabet. For energies below epsilon(c) it is not proven that a g ood symbolic dynamics description exists. We propose and investigate s everal methods to determine a symbolic dynamics, and conjecture that t hese methods label uniquely all non-escaping trajectories for epsilon greater than or equal to 0 and most trajectories for epsilon < 0. We d efine well ordered symbols and construct the pruning front which deter mines the admissible orbits, the information needed for effective semi classical resonance spectra computations.