具有轨道翻转和倾斜翻转的退化异维环分支

Degenerate bifurcations of heterodimensional cycle with orbit flip and inclination flip

本文研究4维系统中一类具有轨道翻转和倾斜翻转的退化异维环分支问题.通过在未扰异维环的小管状邻域内建立局部活动坐标系,本文建立Poincar′e映射,确定分支方程.由对分支方程的分析,本文讨论在小扰动下,异宿环、同宿环和周期轨的存在性、不存在性和共存性,且给出它们的分支曲面以及共存区域,推广了已有结果.

We study the heterodimensional cycle with orbit flip and inclination flip in four-dimensional system. By setting up a new local coordinate system in small tubular neighborhood of unperturbed heterodimensional cycle, we construct a Poincare return map and further obtain the bifurcation equations. Based on the bifurcation analysis, we obtain the condition for the existence and coexistence of the heterodimensional orbit, homoclinic orbit and periodic orbit. Also, the relevant bifurcation surfaces and their existing regions are given. Some known results are extended.