Abstract
We present new proofs of the theorem on the width of the forbidden regions for the Hill equation with a small potential and the theorem on the width of the parametric resonance regions for a first-order differential equation on a torus. These results are special cases of the theorem proved in this paper by the normal form method.
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Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 129–135, July, 1998.
The author wishes to thank M. F. Kondrat'eva, V. V. Sidorenko, and the referee for useful remarks.
This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-01411.
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Sadov, S.Y. Width of parametric resonance regions for equations on a torus. Math Notes 64, 110–115 (1998). https://doi.org/10.1007/BF02307201
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DOI: https://doi.org/10.1007/BF02307201