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.
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.
出处
《厦门大学学报(自然科学版)》
CAS
CSCD
北大核心
2009年第6期800-803,共4页
Journal of Xiamen University:Natural Science
基金
福建省自然科学基金(2006J0208)
福建省教育厅基金(JB08023)
福州大学科技发展基金(2006-XY-17)资助
关键词
无界
全局
非自治系统
拓扑线性化
unbounded
global
non-autonomouse system
topological linearization