  A semiclassical theory is developed and compared to experiments on the
tunneling resonance spectrum for a quantum well in magnetic field tilted with
respect to the tunneling direction. As the tilt angle is increased from zero
the classical mechanics of an electron trapped within the well undergoes a
smooth transition from integrable to chaotic dynamics. Perturbation theory is
invalid for most of the regime of experimental interest, motivating a
semiclassical treatment based on short periodic orbits within the well. In this
paper we present a unified theory of all the periodic orbits within the well
which are of relevance to experiments and show that they are all related to
bifurcations of the period-one traversing orbits. An analytic theory is derived
for the period and stability of these traversing orbits. An unusual feature of
the classical mechanics of this system is the existence of certain important
periodic orbits only in finite energy bands. We calculate the widths of these
bands and relate them to experimental data. In the forthcoming paper the
results for these short periodic orbits are used in conjunction with a novel
semiclassical tunneling formula to calculate the magnetotunneling current,
which is then compared with experiments.
