论文标题
许多数字不变的矢量场家族
Families of vector fields with many numerical invariants
论文作者
论文摘要
我们在$ s^2 $上研究矢量田有限参数家族的分叉。 Yu最近的论文。 Ilyashenko，N。Goncharuk，Yu。 Kudryashov，I。Schurov和N. Solodovnikov提供了（本地通用的）3参数矢量场的（本地通用）属于结构不稳定的家庭：通用的亲密3参数家族经历不同的分叉。在本文中，我们使用这些结果来构建几乎没有参数的平面向量领域的仿制药系列的新示例，以使它们的分类具有许多不变性。特别是，我们构建了（a）具有无限许多数字不变性的3参数家族； （b）任意许多“健壮”数值不变的4参数家族； （c）具有功能不变的5个参数家族。
We study bifurcations in finite-parameter families of vector fields on $S^2$. Recent papers by Yu. Ilyashenko, N. Goncharuk, Yu. Kudryashov, I. Schurov, and N. Solodovnikov provide examples of (locally generic) structurally unstable families of 3-parameter vector fields: generic close 3-parameter families experience different bifurcations. In this paper, we use these results to construct new examples of few-parameter generic families of planar vector fields such that their classification has many invariants. In particular, we construct (a) 3-parameter families with infinitely many numerical invariants; (b) 4-parameter families with arbitrarily many "robust" numerical invariants; (c) 5-parameter families with functional invariants.
