Geodesic
On an almost periodic perturbation on an infinite-dimensional torus
Izvestiya. Mathematics , Tome 28 (1987) no. 3, pp. 609-623.

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A well-known result due to V. I. Arnol'd on the reducibility of a weakly perturbed system of differential equations on a finite-dimensional torus is generalized first to the case when the number of equations is infinite, and, second, to the case when the perturbation is an almost periodic function of time. The reduction is effected by Kolmogorov's method of successive substitutions. Conditions are obtained for the convergence of the method for this problem. It is shown that almost all (in a certain sense) bases of frequencies satisfy the requisite condition. Bibliography: 10 titles 
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D. A. Tarkhov. On an almost periodic perturbation on an infinite-dimensional torus. Izvestiya. Mathematics , Tome 28 (1987) no. 3, pp. 609-623. http://geodesic.mathdoc.fr/item/IM2_1987_28_3_a7/

[1] Arnold V. I., “Malye znamenateli I. Ob otobrazheniyakh okruzhnosti na sebya”, Izv. AN SSSR. Ser. matem., 25:1 (1961), 21–86 | MR

[2] Mozer Yu., “Bystro skhodyaschiisya metod iteratsii i nelineinye differentsialnye uravneniya”, Uspekhi matem. nauk, 23:4 (1968), 178–238 | MR

[3] Samoilenko A. M., “O strukture traektorii na tore”, UMZh, 16:6 (1964), 769–782 | MR

[4] Blinov I. N., “$B$-algebra pochti periodicheskikh funktsii”, Funkts. analiz i ego prilozh., 16:4 (1982), 57–58 | MR | Zbl

[5] Zigel K. L., Lektsii po nebesnoi mekhanike, IL, M., 1959, 302 pp.

[6] Shabat B. V., Vvedenie v kompleksnyi analiz. II, Nauka, M., 1976, 400 pp. | MR

[7] Polia G., Sege G., Zadachi i teoremy iz analiza, t. 2, Nauka, M., 1978, s. 12

[8] Blinov I. N., “Ob odnom klasse ravnomernykh pochti-periodicheskikh funktsii”, Izv. VUZov. Matematika, 1978, no. 2(189), 8–14 | MR | Zbl

[9] Dedonne Zh., Osnovy sovremennogo analiza, Mir, M., 1964, 432 pp.

[10] Shilov G. E., Fan Dyk Tin, Integral, mera i proizvodnaya na lineinykh prostranstvakh, Nauka, M., 1967, 192 pp. | MR