Homoclinic finger-rings in R-N
Homoclinic finger-rings in R-N
复制标题
R-N 中的同宿指环
DOI：
10.1016/j.jde.2017.04.026
复制
发表时间：
2017
影响因子：
2.4
通讯作者：
Zhang Weinian
中科院分区：
文献类型：
--
作者：
Zhu Changrong;Zhang Weinian
本文研究了RN中退化同宿环的分支。我们证明了同宿指环，一个不变流形的一个确定的维数纹理与同宿轨道，产生于退化的同宿轨道。同宿指环的大小不仅取决于它的流形维数，还取决于它的宽度。对于不同维数的同宿指环的出现，给出了在参数空间中形成分歧流形的条件。我们进一步估计了同宿指环的宽度，并给出了一种近似计算分歧流形的方法。
In this paper we investigate bifurcations of a degenerate homoclinic loop in R N. We prove that a homoclinic finger-ring, an invariant manifold of a definite dimension textured with homoclinic orbits, arises from the degenerate homoclinic orbit. The size of the homoclinic finger-ring is decided by not only its dimension of manifold but also its width. For the rise of homoclinic finger-rings of different dimensions we give conditions, which are proved to form bifurcation manifolds in the parameter space. We further estimate the width for the homoclinic finger-ring and give a method to compute the bifurcation manifolds approximately.