指数二分性与自治奇摄动系统的退化同宿分支  

Exponential Dichotomies and Degenerate Homoclinic Bifaroation of Autonomous Singularly Perlurbed Systems

作　　者：张发明[1] 

机构地区：[1]株洲工学院基础部,株洲412008

出　　处：《应用数学》1998年第2期9-16,共8页Mathematica Applicata

摘　　要：利用指数二分性理论和泛函分析方法，我们研究了高维自治奇摄动系统的同、异宿轨道的存在性．给出了高维奇摄动系统从退化系统分支出同异宿轨道的Melnikov型函数．此外，还证明了某一类变分方程在R上具有指数二分性．Using the theory of exponential dichotomies and functional analysis method, we study the existence of homoclinic and heteroclinic orbits of autonomous singularly perturbed systems in high dimension case. We give Melnibov functions of these systems in the case of the bifurcation of homocliuic and heteroclinic orbits from degenerate systems. Moreover, we prove the existence of exponehtial dichotomy of some variational equations in R.

关 键 词：指数二分性 同宿轨道 奇摄动系统 自治系统 

分 类 号：O175.1[理学—数学]