Abstract
We revisit the well known problem of the validity of the averaging principle in multifrequency systems. With analyticity hypotheses, we prove that for initial data satisfying a finite number of nonresonance conditions the slow variables I(t) remain close to the solution I(t) of the averaged system starting from the same initial point. The difference being O( epsilon mod ln epsilon mod a) for times as long as O(1/ epsilon mod ln epsilon mod b), with positive a and b. The set of good initial data is characterized in an explicit way, possibly leading to practical applications.
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