【摘要】 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.更多还原

【Abstract】 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)+ψ(t,y) is discussed.Only if f(t,x),φ(t,x),g(t,y),ψ(t,y) have special structures,the proper homeomorphic 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)+ψ(t,y) onto that of the system v′(A(t)vu′=B(t)u.The result of this pater is more generalized than that of before.更多还原