Study of regular and irregular states in generic systems

In this work we present the results of a numerical and semiclassical analys is of high-lying states in a Hamiltonian system, whose classical mechanics is of a generic, mixed type, where the energy surface is split into regions of regular and chaotic motion. As predicted by the principle of uniform se miclassical condensation, when the effective (h) over bar tends to zero, ea ch state can be classified as regular or irregular. We were able to semicla ssically reproduce individual regular states by the Einstein-Brillouin-Kell er torus quantization, for which we devise a new approach, while for the ir regular ones we found the semiclassical prediction of their autocorrelation function, in a good agreement with numerics. We also looked at the low-lyi ng states to get a better understanding of the onset of semiclassical behav iour.