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Lie equations for asymptotic solutions of perturbation problems of ordinary differential equations. (English) Zbl 1214.34033

Summary: 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.

Editorial remark: No review copy delivered

MSC:
34C14Symmetries, invariants (ODE)
34C20Transformation and reduction of ODE and systems, normal forms
34E05Asymptotic expansions (ODE)
34E15Asymptotic singular perturbations, general theory (ODE)