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

Jing Li; Liying Kou; Duo Wang; Wei Zhang

doi:10.1142/S0218127417502248

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 journal › Article › peer-review

4 Citations (Scopus)

Abstract

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 language	English
Article number	1750224
Journal	International Journal of Bifurcation and Chaos
Volume	27
Issue number	14
DOIs	https://doi.org/10.1142/S0218127417502248
Publication status	Published - 30 Dec 2017
Externally published	Yes

Keywords

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

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10.1142/S0218127417502248

Cite this

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

abstract = "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.",

keywords = "Three-dimensional nilpotent vector field, multiple Lie bracket, transformation with parameters, unique normal form",

author = "Jing Li and Liying Kou and Duo Wang and Wei Zhang",

note = "Funding Information: The research project is supported by National Natural Science Foundation of China (11772007, 11372014, 11072007 and 11290152) and also supported by Beijing Natural Science Foundation (1172002, 1122001). Publisher Copyright: {\textcopyright} 2017 World Scientific Publishing Company.",

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T1 - Unique Normal Form and the Associated Coefficients for a Class of Three-Dimensional Nilpotent Vector Fields

AU - Li, Jing

AU - Kou, Liying

AU - Wang, Duo

AU - Zhang, Wei

N1 - Funding Information: The research project is supported by National Natural Science Foundation of China (11772007, 11372014, 11072007 and 11290152) and also supported by Beijing Natural Science Foundation (1172002, 1122001). Publisher Copyright: © 2017 World Scientific Publishing Company.

PY - 2017/12/30

Y1 - 2017/12/30

N2 - 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.

AB - 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.

KW - Three-dimensional nilpotent vector field

KW - multiple Lie bracket

KW - transformation with parameters

KW - unique normal form

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U2 - 10.1142/S0218127417502248

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M3 - Article

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SN - 0218-1274

VL - 27

JO - International Journal of Bifurcation and Chaos

JF - International Journal of Bifurcation and Chaos

IS - 14

M1 - 1750224

ER -

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

Abstract

Keywords

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