指数二分性与高阶Melnikov函数

EXPONENTIAL DICHOTOMIES AND HIGHER ORDER MELNIKOV FUNCTIONS

本文利用指数二分性理论和Liapunov－Schmidt方法，研究了当Melnikov函数具有高阶零点时的横截同宿轨道的存在性。

Using the theory of exponential dichotomies we study in this paper the existence of transversal homoclinic orbits in the case where the Melnikov function of the systemhas no simple zero. We obtain a so-called higher order Melnikov function.