An improved recursive formula for computing normal forms of multi-dimensional dynamical systems

作者：Guo Lei; Li Qunhong^*; Song Zigen

来源：Journal of Applied Sciences, 2013, 13(15): 2924-2928.

DOI：10.3923/jas.2013.2924.2928

• Computing software
• Higher order terms
• Maple
• Near-identity transformation
• Non-linear transformations
• Normal form
• Recursive formula
• Topology structure

In this study, an improved explicit recursive formula of normal forms under nonlinear near-identity transformations is firstly introduced and the associated proof is also given out. Compared with traditional method, the improved method can get the specific expression of the higher order terms of dynamical systems after nonlinear transformations. So the normal forms of the original dynamical systems can be obtained by a series of nonlinear transformations but without changing its topology structure, also by solving a series of algebra equations with the aid of computing software Maple, not only the coefficients of the jth order normal form and the associated nonlinear transformations but also higher (>j) order terms of the original equations can be obtained. The application of the improved method will greatly simplify the computation during the research of dynamical systems.

• 出版日期2013
• 单位上海海洋大学