一类非线性拟周期系统的约化

On the Reducibility of a Class of Nonlinear Quasi-periodic System

推广了文献[8]的结果,考虑一类带小扰动参数的实解析非线性拟周期系统的约化问题,证明对于绝大多数充分小的扰动参数,在适当的非共振条件下,不需要任何的非退化条件,就可以通过一个仿射的拟周期变换,把系统在零平衡点附近约化成一个适当的标准形。

This paper generalizes the literature [8] and focuses on the reducibility of a class of the real nonlinear analytical quasi-periodic system.With some suitable non-resonant conditions and without any non-degeneracy condition,we change the system into a suitable norm form at the zero equilibrium for the most of the sufficiently small perturbation parameter.