Normal forms of C vector fields based on the renormalization group

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The normal form theory for polynomial vector fields is extended to those for C∞ vector fields vanishing at the origin. Explicit formulas for the C∞ normal form and the near identity transformation that brings a vector field into its normal form are obtained by means of the renormalization group method. The dynamics of a given vector field such as the existence of invariant manifolds is investigated via its normal form. The C∞ normal form theory is applied to prove the existence of infinitely many periodic orbits of two dimensional systems, which is not shown from polynomial normal forms.

Original languageEnglish
Article number062703
JournalJournal of Mathematical Physics
Issue number6
Publication statusPublished - 2021 Jun 1

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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