Geodesic
Width of parametric resonance regions for equations on a torus
Matematičeskie zametki, Tome 64 (1998) no. 1, pp. 129-135 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     author = {S. Yu. Sadov},
     title = {Width of parametric resonance regions for equations on a torus},
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     pages = {129--135},
     year = {1998},
     volume = {64},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_1_a12/}
}
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S. Yu. Sadov. Width of parametric resonance regions for equations on a torus. Matematičeskie zametki, Tome 64 (1998) no. 1, pp. 129-135. http://geodesic.mathdoc.fr/item/MZM_1998_64_1_a12/

[1] Arnold V. I., “Zamechaniya o teorii vozmuschenii dlya zadach tipa Mate”, UMN, 38:4 (1983), 189–203 | MR | Zbl

[2] Arnold V. I., Ilyashenko Yu. S., “Obyknovennye differentsialnye uravneniya”, Dinamicheskie sistemy – I, Itogi nauki i tekhn. Sovrem. probl. matem. Fundament. napravleniya, 1, VINITI, M., 1985, 7–140

[3] Galkin O. G., “Resonance regions for Mathieu type dynamical systems on a torus”, Phys. D, 39 (1989), 287–298 | DOI | MR | Zbl

[4] Galkin O. G., “Fazovyi zakhvat dlya vektornykh polei na tore tipa Mate”, Funktsion. analiz i ego prilozh., 26:1 (1992), 1–8 | MR | Zbl

[5] Galkin O. G., “Fazovyi zakhvat dlya otobrazhenii tora tipa Mate”, Funktsion. analiz i ego prilozh., 27:1 (1992), 1–11 | MR

[6] Sadov S. Yu., Ploskie dvizheniya pochti simmetrichnogo sputnika otnositelno tsentra mass s ratsionalnymi chislami vrascheniya, Preprint No 31, IPM im. M. V. Keldysha RAN, M., 1997

[7] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | Zbl