Abstract
We develop a new method to include intermittency into the periodic orbit description of a dynamical system. The technique allows removal of typical singularities in classical and semiclassical zeta functions caused by the coexistence of regular and chaotic dynamics. Approximate quantum numbers are derived from the regular dynamics, which provide a natural connection between periodic orbit theory and the semiclassical quantization of integrable systems. Interference effects and level repulsion in the quantum spectrum are resolved by including the classical chaotic dynamics in a perturbation expansion. Results are given for the Rydberg series structures in $S$ helium.
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