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

作者：Li, Jing; Zhang, Lina; Wang, Duo^*

来源：Journal of Differential Equations, 2014, 257(7): 2341-2359.

DOI：10.1016/j.jde.2014.05.039

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

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.

• 出版日期2014-10-1
• 单位华南师范大学; 北京大学; 北京工业大学