Abstract
We discuss symbolic dynamics for the Hamiltonian describing the classical motion of hydrogen in a uniform magnetic field with zero angular momentum. For a scaled energy above a critical value , the Hamiltonian has a Cantor set repellor described by a three-lettered symbolic alphabet. For energies below it is not proven that a good symbolic dynamics description exists. We propose and investigate several methods to determine a symbolic dynamics, and conjecture that these methods label uniquely all non-escaping trajectories for and most trajectories for . We define well ordered symbols and construct the pruning front which determines the admissible orbits, the information needed for effective semiclassical resonance spectra computations.
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