  The existence of periodic orbit bunches is proven for the diamagnetic Kepler
problem. Members of each bunch are reconnected differently at self-encounters
in phase space but have nearly equal classical action and stability parameters.
Orbits can be grouped already on the level of the symbolic dynamics by
application of appropriate reconnection rules to the symbolic code in the
ternary alphabet. The periodic orbit bunches can significantly improve the
efficiency of semiclassical quantization methods for classically chaotic
systems, which suffer from the exponential proliferation of orbits. For the
diamagnetic hydrogen atom the use of one or few representatives of a periodic
orbit bunch in Gutzwiller's trace formula allows for the computation of
semiclassical spectra with a classical data set reduced by up to a factor of
20.
