BIFURCATIONS OF PERIODIC-ORBITS AND UNIFORM APPROXIMATIONS

We derive uniform approximations for contributions to Gutzwiller's per iodic-orbit sum For the spectral density which are valid close to bifu rcations of Periodic orbits in systems with mixed phase space. There, orbits lie close together and give collective contributions, while the individual contributions of Gutzwiiler's type would diverge at the bi furcation. New results for the tangent, the period-doubling and the pe riod-tripling bifurcation are given. They are obtained by going beyond the local approximation and including higher-order terms in the norma l form of the action. The uniform approximations obtained are tested o n the kicked top and are found to be in excellent agreement with exact quantum results.