非自治系统的拓扑线性化

The Topological Linearization of Nonautonomous Systems

微分方程拓扑线性化理论是由Hart man和Grobman给出的,Pal mer把线性化理论推广到了非自治系统.对非自治系统的拓扑线性化理论进行扩展,讨论了系统x′=A(t)x+f(t,x)+g(t,y)y′=B(t)y+φ(t,x)+ψ(t,y)的线性化.当f(t,x)、φ(t,x)、g(t,y)、ψ(t,y)具有特殊结构时,通过构造适当的同胚函数,把系统x′=A(t)x+f(t,x)+g(t,y)y′=B(t)y+φ(t,x)+ψ(t,y)的解映射为系统vu′′==BA((tt))uv的解.所讨论的系统更常见,结论更实用.

Hartman and Grobman proposed the concept of topological linearization. Later, Palmer generalized the concept to the non- autonomouse case. This paper generalizes the result of topological linearization. The topological linearization of the system {x′=A（t）x＋f（t,x）＋g（t,y） y′=B（t）y＋φ（t,x）＋φ（t,y）is discussed. Only if f（t,x）、φ（t,x）、g（t,y）、φ（t,y） have special structures,the proper homeomor-phic function can map the solution of the system {x′=A（t）x＋f（t,x）＋g（t,y） y′=B（t）y＋φ（t,x）＋φ（t,y）onto that of the system{v′=A（t）v u′=B（t）u. The result ofthis pater is more generalized than that of before.