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Multidegree of freedom nonlinear differential equations can often be transformed by means ofthe method of averaging into equivalent systems with only high-order terms. Under appropriate small-order perturbation conditions these systems have unique surfaces of solutions called integral manifolds. They generalize the notions of periodic and almost periodic solutions for single degree of freedom systems. In parametric form the integral manifolds satisfy a certain system of partial differentialdoi:10.1137/0147061 fatcat:2z7wrfo3nvbbdedmcgey2fcl54