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Unique normal form of a class of 3 dimensional vector fields with symmetries |
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| Authors: | Jing Li Lina Zhang Duo Wang |
| Affiliation: | 1. College of Applied Sciences, Beijing University of Technology, Beijing 100124, PR China;2. School of Mathematical Sciences, Peking University, Beijing 100871, PR China;3. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, PR China |
| 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&ndash Takens-zero singularity Unique normal form Linear grading function Multiple Lie brackets New notation of block matrices |
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