Abstract
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.
Original language | English |
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Article number | 1750131 |
Journal | International Journal of Bifurcation and Chaos |
Volume | 27 |
Issue number | 8 |
DOIs | |
Publication status | Published - 1 Jul 2017 |
Externally published | Yes |
Keywords
- Three-dimensional nilpotent vector field
- first integral
- linear grading function
- multiple Lie brackets
- unique normal form