| 非自治系统的拓扑线性化 |
| |
| 引用本文： | 邹长武,蔡国财.非自治系统的拓扑线性化[J].厦门大学学报(自然科学版),2009,48(6). |
| |
| 作者姓名： | 邹长武 蔡国财 |
| |
| 作者单位： | 1. 福州大学数学系,福建,福州,350108
2. 厦门大学数学科学学院,福建,厦门,361005 |
| |
| 基金项目： | 福建省自然科学基金，福建省教育厅基金，福州大学科技发展基金 |
| |
| 摘 要： | 微分方程拓扑线性化理论是由Hartman和Grobman给出的,Palmer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{v′=A(t)v u′=B(t)u的解.所讨论的系统更常见,结论更实用.
|
| 关 键 词： | 无界 全局 非自治系统 拓扑线性化 |
The Topological Linearization of Nonautonomous Systems |
| |
| ZOU Chang-wu,CAI Guo-cai.The Topological Linearization of Nonautonomous Systems[J].Journal of Xiamen University(Natural Science),2009,48(6). |
| |
| Authors: | ZOU Chang-wu CAI Guo-cai |
| |
| 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)v u′=B(t)u.The result of this pater is more generalized than that of before . |
| |
| Keywords: | unbounded global non-autonomouse system topological linearization |
| 本文献已被 万方数据 等数据库收录！ |
|
