Abstract
The author obtains an unimprovable estimate of the averaging method for a two-frequency problem with analytic right-hand sides under condition , which means a nonzero rate of change of the frequency ratio along trajectories of the averaged system. It turns out to be of order for initial data outside a set of measure of order , where is a small parameter of the problem and is an upper bound for the maximal multiplicity of the roots of a certain finite set of equations (it is assumed that ).Bibliography: 8 titles.
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