Melnikov向量和一般退化同宿分支

Melnikov Vector and a General Degenerate Homoclinic Bifurcations

利用指数型二分性理论和泛函分析方法，讨论了一般退化情形下的同宿分支理论，得到了一个一般的Ｍｅｌｎｉｋｏｖ型向量，且证明由此Ｍｅｌｎｉｋｏｖ向量的简单零点可推出横截同宿轨道的存在性．

This paper mainly studies the theory of homoclinic bifurcations in a degenerate case by using the theory of exponential dichotomise. We obtain a Melnikov like vector by which the existence of homoclnic orbits can be dectecd.