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JOURNALS // Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya // Archive

Izv. Akad. Nauk SSSR Ser. Mat., 1986 Volume 50, Issue 3, Pages 617–632 (Mi im1522)

This article is cited 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

UDC: 517.928+517.937

MSC: Primary 58F30; Secondary 34C50, 34C40, 34C20

Received: 23.01.1984


 English version:
Mathematics of the USSR-Izvestiya, 1987, 28:3, 609–623

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