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Zbl 1214.34033
Chiba, Hayato; Iwasa, Masatomo
Lie equations for asymptotic solutions of perturbation problems of ordinary differential equations. (English)
[J] J. Math. Phys. 50, No. 4, 042703, 18 p. (2009). ISSN 0022-2488; ISSN 1089-7658/e

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 {\it M. Iwasa} and {\it 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 2000:: *34C14 Symmetries, invariants
34C20 Transformation of ODE and systems
34E05 Asymptotic expansions (ODE)
34E15 Asymptotic singular perturbations, general theory (ODE)

Keywords: differential equations; initial value problems; Lie groups; perturbation theory

Citations: Zbl 1108.81040

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Zentralblatt MATH Berlin [Germany]