Melinkov向量和退化情形下的同宿分支

Melnikov Vector and Homoclinic Bifurcations in a Degenerate Case

本文研究了微分方程在退化情形下的同宿分支，通过利用指数型二分性理论和ＬｉａｐｕｎｏｖＳｃｈｍｉｄｔ方法，我们获得Ｍｅｌｎｉｋｏｖ型向量，通过它可以确定同宿轨道的存在性。

The main purpose of this paper is to study homoclinic bifurcation in a degenerate case of differential equations of form x=f(x,ε) and x=g(x) +h (t,x,ε). By using theory of exponential dichotomise and Liapunov-Schmidt method, we obtain the Melnikov-like vectors by which the existence of homoclinic orbits can be detected.