Normal forms and uniform approximations for bridge orbit bifurcations

Abstract

We discuss various bifurcation problems in which two isolated periodic orbits exchange periodic ``bridge'' orbit(s) between two successive bifurcations. We propose normal forms which locally describe the corresponding fixed point scenarios on the Poincare surface of section. Uniform approximations for the density of states for a two-dimensional integrable system are derived and successfully reproduce the numerical quantum-mechanical results.