同宿轨向量场的特征扰动空间

Characteristic perturbation space for a vector field with homoclinic orbits

为了研究同宿轨向量场的一个新的扰动现象,通过高阶Melnikov函数,构造了一类同宿轨向量场的特征扰动空间,使得在此空间中的函数的扰动下,向量场的同宿轨依然存在,并证明了该特征扰动空间为Banach空间.这个结果进一步完善了同宿轨向量场理论.

It was mainly studied a new perturbation phenomenon on vector field with homoclinic orbits. By high order Melnikov functions,the characteristic perturbation space was obtained. The homoclinic orbits were showed still existed by the perturbation from the functions in this space. Finally the characteristic perturbation space was proved to be a Banach space. This result provides the theory of the vector field with homoclinic orbits a further improvement.