伴随超临界分支的通有同宿轨道分支

Bifurcation of Generic Homoclinic Orbit Accompanied with Transcritical Bifurcation

本文研究具有非双曲奇点的高维系统在小扰动下的同宿轨道分支问题,通过在未扰同宿轨道邻域建立局部坐标系,导出系统在新坐标系下的Poincare映射,对伴随超临界分支的通有同宿轨道的保存及分支出周期轨道的情况进行了讨论,推广和改进了一些文献的结果.

The problem of homoclinic bifurcation under perturbation is studied for the high dimensional system with nonhyperbolic equilibrium. By constructing local coordinate systems near the unperburbed homoclinic orbit, we get Poincare maps of the system in new coordinate systems, and discuss the persistence of generic homoclinic orbit and the bifurcation of periodic orbit from the homoclinic orbit for the system accompanied with transcritical bifurcation. Some known results are extended.