Unique normal form of a class of 3 dimensional vector fields with symmetries

Jing Li; Lina Zhang; Duo Wang

doi:10.1016/j.jde.2014.05.039

Unique normal form of a class of 3 dimensional vector fields with symmetries

Jing Li
, Lina Zhang
, Duo Wang^*

^*Corresponding author for this work

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

37 Citations (Scopus)

Abstract

We present the unique normal form of a class of 3 dimensional vector fields (BT-zero singularity) with symmetries. The main technique applied to the computation is the combination of a linear grading function and the method of multiple Lie brackets. We introduce new notations for block matrices to simplify the expression of block matrices. The new notations help to prove the non-degeneracy of huge size matrices by an induction technique.

Original language	English
Pages (from-to)	2341-2359
Number of pages	19
Journal	Journal of Differential Equations
Volume	257
Issue number	7
DOIs	https://doi.org/10.1016/j.jde.2014.05.039
Publication status	Published - 1 Oct 2014
Externally published	Yes

Keywords

3 dimensional vector fields
Bogdanov-Takens-zero singularity
Linear grading function
Multiple Lie brackets
New notation of block matrices
Unique normal form

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10.1016/j.jde.2014.05.039

Cite this

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title = "Unique normal form of a class of 3 dimensional vector fields with symmetries",

abstract = "We present the unique normal form of a class of 3 dimensional vector fields (BT-zero singularity) with symmetries. The main technique applied to the computation is the combination of a linear grading function and the method of multiple Lie brackets. We introduce new notations for block matrices to simplify the expression of block matrices. The new notations help to prove the non-degeneracy of huge size matrices by an induction technique.",

keywords = "3 dimensional vector fields, Bogdanov-Takens-zero singularity, Linear grading function, Multiple Lie brackets, New notation of block matrices, Unique normal form",

author = "Jing Li and Lina Zhang and Duo Wang",

note = "Funding Information: The authors gratefully acknowledge the support of the National Natural Science Foundation of China through Grant No. 11072007 , No. 11372014 , No. 10871005 and No. 11290152 , the Natural Science Foundation of Beijing through Grant No. 1122001 and the International Science \& Technology Cooperation Program of China through Grant No. 2014DFR61080 . They also thank Dr. X-B Lin for reading through the paper and pointing out some errors in English usage.",

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doi = "10.1016/j.jde.2014.05.039",

language = "English",

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T1 - Unique normal form of a class of 3 dimensional vector fields with symmetries

AU - Li, Jing

AU - Zhang, Lina

AU - Wang, Duo

N1 - Funding Information: The authors gratefully acknowledge the support of the National Natural Science Foundation of China through Grant No. 11072007 , No. 11372014 , No. 10871005 and No. 11290152 , the Natural Science Foundation of Beijing through Grant No. 1122001 and the International Science & Technology Cooperation Program of China through Grant No. 2014DFR61080 . They also thank Dr. X-B Lin for reading through the paper and pointing out some errors in English usage.

PY - 2014/10/1

Y1 - 2014/10/1

N2 - We present the unique normal form of a class of 3 dimensional vector fields (BT-zero singularity) with symmetries. The main technique applied to the computation is the combination of a linear grading function and the method of multiple Lie brackets. We introduce new notations for block matrices to simplify the expression of block matrices. The new notations help to prove the non-degeneracy of huge size matrices by an induction technique.

AB - We present the unique normal form of a class of 3 dimensional vector fields (BT-zero singularity) with symmetries. The main technique applied to the computation is the combination of a linear grading function and the method of multiple Lie brackets. We introduce new notations for block matrices to simplify the expression of block matrices. The new notations help to prove the non-degeneracy of huge size matrices by an induction technique.

KW - 3 dimensional vector fields

KW - Bogdanov-Takens-zero singularity

KW - Linear grading function

KW - Multiple Lie brackets

KW - New notation of block matrices

KW - Unique normal form

UR - https://www.scopus.com/pages/publications/84904063522

U2 - 10.1016/j.jde.2014.05.039

DO - 10.1016/j.jde.2014.05.039

M3 - Article

AN - SCOPUS:84904063522

SN - 0022-0396

VL - 257

SP - 2341

EP - 2359

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 7

ER -

Unique normal form of a class of 3 dimensional vector fields with symmetries

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Keywords

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