Semiclassical energy spectrum of quasi-integrable systems

This paper presents the general method for deriving transitional periodic orbit amplitudes near a bifurcation in its simplest instance - the quasi-integrable system. The main qualitative result is that, for sufficiently small perturbations, the semiclassical amplitude smooths over the details of the classical motion - the amplitude may be given correctly by the Berry-Tabor formula on a 'quasi-torus' even when the periodic torus has ceased to exist. The concluding Section analyses the equivalence of torus quantization and the periodic orbit sum. This results in criteria for the validity of applying the former method to quasi-integrable systems