平面约束微分系统在拓扑等价下的分类
On the classification of planar constrained differential systems under topological equivalence
摘要：
本文研究了解析约束微分系统（或绝境系统）的局部解，其形式为$A(x)\dot{x} = F(x)$，$x\in\mathbb{R}^{2}$，其中$F$是向量场，$A$是矩阵值函数.使用技术的奇点的分解加权爆破，我们扩展了著名的结果在文献中的拓扑分类的平面向量场的相图的上下文中这样的系统类。我们还研究了约束系统在所谓的绝境集$Δ=\{x:\det A (x) = 0\}$的奇点附近的相图，并对其进行了分类。
英文摘要：
This paper concerns the local study of analytic constrained differential systems (or impasse systems) of the form $A(x)\dot{x} = F(x)$, $x\in\mathbb{R}^{2}$, where $F$ is a vector field and $A$ is a matrix valued function. Using techniques of resolution of singularities with weighted blow ups, we extend well-known results in the literature on topological classification of phase portraits of planar vector fields to the context of such class of systems. We also study and classify phase portraits of constrained systems near singular points of the so called impasse set $Δ=\{x:\det A (x) = 0\}$.
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