TY - JOUR
T1 - Unique Normal Form for a Class of Three-Dimensional Nilpotent Vector Fields
AU - Li, Jing
AU - Kou, Liying
AU - Wang, Duo
N1 - Publisher Copyright:
© 2017 World Scientific Publishing Company.
PY - 2017/7/1
Y1 - 2017/7/1
N2 - 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.
AB - 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.
KW - Three-dimensional nilpotent vector field
KW - first integral
KW - linear grading function
KW - multiple Lie brackets
KW - unique normal form
UR - http://www.scopus.com/inward/record.url?scp=85027139332&partnerID=8YFLogxK
U2 - 10.1142/S0218127417501310
DO - 10.1142/S0218127417501310
M3 - Article
AN - SCOPUS:85027139332
SN - 0218-1274
VL - 27
JO - International Journal of Bifurcation and Chaos
JF - International Journal of Bifurcation and Chaos
IS - 8
M1 - 1750131
ER -