AI 中文总结
该研究针对ℝ³原点处实向量场的完全退化芽，构造通用三参数展开并确定局部分岔，证明其相图含连接双曲平衡点的单参数异宿轨道族。
AI 中文摘要
本研究分析ℝ³原点处实向量场的完全退化芽，构造该芽的通用三参数展开并确定相关局部分岔，证明展开系统的相图包含连接两个双曲平衡点的异宿轨道的单参数族。
英文摘要
In this work, we analyze a completely degenerate germ of a real vector field at the origin of $\mathbb{R}^3$. We construct a generic three-parameter unfolding of this germ and identify the associated local bifurcations. We prove that the phase portrait of the unfolded system contains a one-parameter family of heteroclinic orbits connecting two hyperbolic equilibrium points.
Comments10 pages
