Unique Normal Form and the Associated Coefficients for a Class of Three-Dimensional Nilpotent Vector Fields

Jing Li*, Liying Kou, Duo Wang, Wei Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


In this paper, we mainly focus on the unique normal form for a class of three-dimensional vector fields via the method of transformation with parameters. A general explicit recursive formula is derived to compute the higher order normal form and the associated coefficients, which can be achieved easily by symbolic calculations. To illustrate the efficiency of the approach, a comparison of our result with others is also presented.

Original languageEnglish
Article number1750224
JournalInternational Journal of Bifurcation and Chaos
Issue number14
Publication statusPublished - 30 Dec 2017
Externally publishedYes


  • Three-dimensional nilpotent vector field
  • multiple Lie bracket
  • transformation with parameters
  • unique normal form

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