Spectra for semiclassical operators with periodic bicharacteristics in dimension two

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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 ε of the perturbation is ≪ h, the spectrum displays a cluster structure, and assuming that ε ≫ h² (or sometimes ≫ hⁿ⁰, for N₀ >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.