Significance of ghost orbit bifurcations in semiclassical spectra

Gutzwiller's trace formula for the semiclassical density of states in a cha otic system diverges near bifurcations of periodic orbits, where it must be replaced with uniform approximations. It is well known that, when applying these approximations, complex predecessors of orbits created in the bifurc ation ('ghost orbits') can produce pronounced signatures in the semiclassic al spectra in the vicinity of the bifurcation. It is the purpose of this pa per to demonstrate that these ghost orbits can also undergo bifurcations, r esulting in complex, nongeneric bifurcation scenarios. We do so by studying an example taken from the diamagnetic Kepler problem, namely the period qu adrupling of the balloon orbit. By application of normal form theory we con struct an analytic description of the complete bifurcation scenario, which is then used to calculate the pertinent uniform approximation. The ghost or bit bifurcation turns out to produce signatures in the semiclassical spectr um in much the same way as a bifurcation of real orbits would.