TY - JOUR
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 - http://www.scopus.com/inward/record.url?scp=84904063522&partnerID=8YFLogxK
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 -