CONTENTSIntroduction ??1. Rayleigh-Schr?dinger series for perturbations of a simple eigenvalue ??2. Perturbations of a multiple eigenvalue ??3. Widths of forbidden zones of even Hill's equations of Mathieu type ??4. Formulae for the denominators of terms in the perturbation theory series ??5. Conclusion of the investigation of forbidden zones ??6. Widths of resonance zones for mappings of the circleReferences
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Vladimir I. Arnold (1983) studied this question.