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

Hayato Chiba, Masatomo Iwasa

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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 Iwasa and Nozaki ["A method to construct asymptotic solutions invariant under the renormalization group," Prog. Theor. Phys. 116, 605 (2006)]. 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.

Original languageEnglish
Article number042703
JournalJournal of Mathematical Physics
Volume50
Issue number4
DOIs
Publication statusPublished - 2009 May 18
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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