一类广义鞍结平面系统正规形的计算  

Computation of Normal Forms for a Type of Generalized Planar Saddle-node System

作　　者：李梦晓[1] 黄土森[1] 

机构地区：[1]浙江理工大学理学院,杭州310018

出　　处：《浙江理工大学学报（自然科学版）》2017年第1期116-121,共6页Journal of Zhejiang Sci-Tech University(Natural Sciences)

基　　金：浙江省自然科学基金项目(LY15A010021)

摘　　要：对于一类广义鞍结系统,利用Carleman线性化方法,把非线性系统转化为无穷维上的线性系统,得到矩阵中具体项之间的递推关系,从而计算出它的正规形,并给出相应的近恒等变量变换。文章提出的计算方法和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动力系统的正规形情形;从计算过程中可以直接得出相应的近恒等变量变换,从而解决了经典正规形理论中只能在理论上说明相应近恒等变量变换的存在却无法给出具体变换的难题。该文结果为简化分析这类退化系统的动力学性质奠定基础。For a type of generalized saddle-node system, nonlinear system is transformed to linear system on the infinite dimension by using the method of Carleman linearization. In this way, the recursive relation among the terms in the matrix the system is obtained and then its normal forms are computed. At the same time, the corresponding nearly identical transformation of variables is given. The calculation method and results in this paper generalize the computation of normal forms for non-linear differential equations with non-zero linear part in the classic theory of normal forms to that with zero linear part. The corresponding nearly identical transformation of variables can be directly gained from the calculation process, which solves the problem that classical theory of normal forms can explain the existence of nearly identical transformation of variables only in theory but cannot give the specific transformation. The results in this paper lay a foundation for simplify analyses of the dynamical behaviors of such type of degenerate system.

关 键 词：广义鞍结系统 正规形 近恒等变量变换 Carlcman方法 

分 类 号：O175.14[理学—数学]