Spectra For Semiclassical Operators With Periodic Bicharacteristics In Dimension Two

We study the distribution of eigenvalues for selfadjoint h-pseudodifferential operators in dimension two, arising as perturbations of selfadjoint operators with a periodic classical flow. When the strength epsilon of the perturbation is << h, the spectrum displays a cluster structure, and assuming that epsilon >> h(2) (or sometimes >> h(N0), for N-0 > 1 large), we obtain a complete asymptotic description of the individual eigenvalues inside subclusters, corresponding to the regular values of the leading symbol of the perturbation, averaged along the flow.