指数二分性与自治奇摄动系统的退化同宿分支

Degenerated Reappearing Orbit of Auto-odd-perturbation System and Index Dichotomy Character

利用指数二分性理论和泛函分析方法，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。

With the theory of dichotomy and functional analysis,the au thors demonstrate the existance of reappearing orbit and varying orbit in multi ple auto-odd-perturbation system. Melnikov function of the appearing orbit and varying orbit is also put forward. At the end,the writers add index dichotomy in a kind of equation of variation.