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This article is cited in 1 scientific paper (total in 1 paper)
On an almost periodic perturbation on an infinite-dimensional torus
D. A. Tarkhov
Abstract:
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
Received: 23.01.1984
Citation:
D. A. Tarkhov, “On an almost periodic perturbation on an infinite-dimensional torus”, Izv. Akad. Nauk SSSR Ser. Mat., 50:3 (1986), 617–632; Math. USSR-Izv., 28:3 (1987), 609–623
Linking options:
https://www.mathnet.ru/eng/im1522https://doi.org/10.1070/IM1987v028n03ABEH000905 https://www.mathnet.ru/eng/im/v50/i3/p617
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Abstract page: | 288 | Russian version PDF: | 93 | English version PDF: | 9 | References: | 50 | First page: | 3 |
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