自治奇摄动系统的同、异宿轨道(英文)

Homoclinic and Heteroclinic Orbit of Auto-Odd-Perturbation System

利用指数二分性理论和泛函分析方法来处理第一变分方程在R上有多于一个非平凡有界解下的奇摄动系统的同宿轨道分支问题.利用此方法我们给出了判断奇摄动系统在退化情形下存在同、异宿轨道的Melnikov向量函数并给出了存在同宿轨道的参数估计范围.

With the theory of dichotomy and functional analysis, the paper studies the homoclinic orbits bifurcation of the Auto-（）dd.-Perturbation System of the first variational equation that has more than one non-trivial bounded solution. By using this method, the paper obtains the Melnikovlike vectors function by which the existence of Homoclinic and Heteroclinic Orbits of this system in a degenerate case can be detected and parameter estimation of the existence of homoclinic orbits.