Geodesic
On integral manifolds of multifrequency oscillatory systems
Izvestiya. Mathematics , Tome 36 (1991) no. 2, pp. 391-409.

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Conditions are found for the existence of an integral manifold for a nonlinear oscillatory system with slowly varying frequencies, and an algorithm for constructing it is described. A theorem is proved on the conditional asymptotic stability of the integral manifold with respect to a set of initial values for the slow variables. Smoothness is also studied, and bounds on the partial derivatives of the function that describes the integral manifold are obtained. 
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A. M. Samoilenko; R. I. Petrishin. On integral manifolds of multifrequency oscillatory systems. Izvestiya. Mathematics , Tome 36 (1991) no. 2, pp. 391-409. http://geodesic.mathdoc.fr/item/IM2_1991_36_2_a8/

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