Normal forms of C vector fields based on the renormalization group

研究成果: Article査読

抄録

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.

本文言語English
論文番号062703
ジャーナルJournal of Mathematical Physics
62
6
DOI
出版ステータスPublished - 2021 6 1

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学

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