Application of an arbitrarily rapidly convergent method to the reducibility problem for linear systems with odd almost-periodic coefficients

We consider a method of successive substitution generalizing the known Kolmogorov–Arnol'd method so as to be applicable in a proof of the reducibility of linear systems with odd almost-periodic coefficients. We prove that our method can be made to converge arbitrarily rapidly. The method is used to solve a problem that cannot be solved by the Kolmogorov–Arnol'd method because of the relatively slow convergence of the latter.mplex.