On an almost periodic perturbation on an infinite-dimensional torus

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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