一类退化平面系统的正规形的计算
An Algorithm for Computing a Normal Form of a Class of Planar Degenerate Dynamical Systems
摘要: 本文利用Carleman线性化方法计算了一类平面退化系统的正规形，并给出相应的近恒等变量变换。这些结果把经典正规形理论中只能计算具非零线性部分动力系统的正规形推广到可以计算具零线性部分系统的正规形情形，为简化分析这类退化系统的动力学性质建立了基础。
Abstract: In this paper the normal forms of a class of planar degenerate dynamical systems are computed by using the method of Carleman linearlization, in the mean time, a sequence of the associated near identity change of variables is given. These results generalize the computations of normal forms for the non-degenerate dynamical systems with non-zero linear part in the classical theory of normal forms to those for the degenerate dynamical systems with zero linear part, and establish the bases to simplify the analyses of the dynamical properties of the degenerate systems.
文章引用：李梦晓, 黄土森. 一类退化平面系统的正规形的计算[J]. 应用数学进展, 2016, 5(1): 98-111. http://dx.doi.org/10.12677/AAM.2016.51014

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