  For singular perturbation problems in dynamical systems, various appropriate
singular perturbation methods have been proposed to eliminate secular terms
appearing in the naive expansion. For example, the method of multiple time
scales, the normal form method, center manifold theory, the renormalization
group method are well known. In this paper, it is shown that all of the
solutions of the reduced equations constructed with those methods are exactly
equal to sum of the most divergent secular terms appearing in the naive
expansion. For the proof, a method to construct a perturbation solution which
differs from the conventional one is presented, where we make use of the theory
of Lie symmetry group.
