Lie equations for asymptotic solutions of perturbation problems of ordinary differential equations.

*(English)*Zbl 1214.34033Summary: Lie theory is applied to perturbation problems of ordinary differential equations to construct approximate solutions and invariant manifolds according to the renormalization group approach of *M. Iwasa* and *K. Nozaki* [Prog. Theor. Phys. 116, No. 4, 605–613 (2006; Zbl 1108.81040)]. It is proved that asymptotic behavior of solutions is obtained from the Lie equations even if original equations have no symmetries. Normal forms of the Lie equations are introduced to investigate the existence of invariant manifolds.

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