Unique Normal Form for a Class of Three-Dimensional Nilpotent Vector Fields

Jing Li; Liying Kou; Duo Wang

doi:10.1142/S0218127417501310

Unique Normal Form for a Class of Three-Dimensional Nilpotent Vector Fields

Jing Li, Liying Kou, Duo Wang^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

In this paper, the unique normal form for a class of three-dimensional nilpotent vector fields with symmetry is investigated. The key technique used is a combination of multiple Lie brackets, linear grading function, new notations of block matrices and first integral of the linear part of the given vector field which avoids complicated calculations. The first and the second order normal forms are computed successively, and the uniqueness of the second order normal form is proved under certain conditions.

Original language	English
Article number	1750131
Journal	International Journal of Bifurcation and Chaos
Volume	27
Issue number	8
DOIs	https://doi.org/10.1142/S0218127417501310
Publication status	Published - 1 Jul 2017
Externally published	Yes

Keywords

Three-dimensional nilpotent vector field
first integral
linear grading function
multiple Lie brackets
unique normal form

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10.1142/S0218127417501310

Cite this

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KW - first integral

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KW - multiple Lie brackets

KW - unique normal form

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Unique Normal Form for a Class of Three-Dimensional Nilpotent Vector Fields

Abstract

Keywords

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