高维自治Birkhoff系统奇点类型及其稳定性

Type and Stability of Singular Points of Higher Order Autonomous Birkhoff System

研究了高维自治Birkhoff系统的奇点类型及其稳定性,首先由奇点方程得到系统的奇点及其性质,然后研究了奇点处Fréchet导数的特征根性质,从而判断出高维自治Birkhoff系统的奇点不存在汇和源,只存在双曲奇点.并给出判断奇点稳定性的相关定理.

The type and stability of singular points of higher order autonomous Birkhoff system are studied. Firstly, the singular points and their properties are obtained from the equations of singular points. Then, the characteristic roots of Fréchet derivative of singular points are researched, and it is found that the singular points of the system are hyperbolic singular points, not sinks or sources. Finally, the theorems of stability of the singular points are given. Key words：