一类平面3次扩展拟齐次系统的分岔

Bifurcation of a class of extended quasi-homogeneous polynomial differential systems

本文研究一类平面3次扩展拟齐次多项式微分系统的分岔问题;证明在3参数族(a,b,c)∈R^3中,此系统不存在极限环;运用拟齐次吹胀(blow-up)和无穷远奇点的Poincaré-Lyapunov紧化等方法,给出系统的全局拓扑相图.

In this paper, we study the bifurcation of a class of extended quasi-homogeneous planar polynomial differential systems of degree 3, prove that this system has no limit cycle in （a, b, c） ∈ R3 and provide its global portraits by using quasi-homogeneous blow-up, Poincare-Lyapunov compactification etc.