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On an almost periodic perturbation on an infinite-dimensional torus
D. A. Tarkhov
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.
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Mathematics of the USSR-Izvestiya, 1987, 28:3, 609–623
MSC: Primary 58F30; Secondary 34C50, 34C40, 34C20
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
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\paper On an almost periodic perturbation on an infinite-dimensional torus
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
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This publication is cited in the following articles:
D. A. Tarkhov, “Reducibility of a linear system of differential equations with odd almost periodic coefficients”, Math. Notes, 60:1 (1996), 81–88
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