Ghost Orbit Bifurcations in Semiclassical Spectra

Gutzwiller's semiclassical trace formula for the density of states in achaotic system diverges near bifurcations of periodic orbits, where it must bereplaced with uniform approximations. It is well known that, when applyingthese approximations, complex predecessors of orbits created in the bifurcation(``ghost orbits'') can produce clear signatures in the semiclassical spectra.We demonstrate that these orbits themselves can undergo bifurcations, resultingin complex, non-generic bifurcation scenarios. We do so by studying an exampletaken from the Diamagnetic Kepler Problem. By application of normal formtheory, we construct an analytic description of the complete bifurcationscenario, which is then used to calculate the pertinent uniform approximation.The ghost orbit bifurcation turns out to produce signatures in thesemiclassical spectrum in much the same way as a bifurcation of real orbitswould.Comment: 10 pages, 6 figures, PTP LaTeX style; contribution to the Summer School/Conference 'Let's Face Chaos through Nonlinear Dynamics', Maribor, Slovenia, June/July 199