一类非线性系统的中心流形与重整化群方法

Center Manifold of a Class of Nonlinear Dynamical System and Renormalization Group Method

利用重整化群方法,给出方程dx/dt=f(x,y),dy/dt=Ay+g(x,y),(x,y)∈Rm×Rn在平衡点(0,0)处中心流形的一致有效逼近.其中:A是n阶可对角化矩阵,其特征值都有负实部;f(x,y)和g(x,y)是Cr(r≥3)向量值函数,满足f(εx,εy)=O(ε2),g(εx,εy)=O(ε2),这里ε>0.

Using the renormalization group method,we gave the uniformly valid asymptotic expansion for the center manifold on the fixed point（0,0）of the following equations dx/dt=f（x,y）, dy/dt=Ay＋g（x,y）,（x,y）∈ Rm× Rn,where Ais an n×ndiagonalizable matrix with all the eigenvalues having negative real parts,f（x,y）and g（x,y）are Cr（r≥3）functions,with f（εx,εy）=O（ε2）,g（εx,εy）=O（ε^2）,here ε〉0.