论文标题
3D尖折的奇异性及其展开的规范形式
Canonical forms of 3d cusp-fold singularities and its unfoldings
论文作者
论文摘要
在本文中，我们获得了32个典型的形式，用于3D分段平滑矢量场，呈现出所谓的尖折。所有这些规范的形式在拓扑上是截然不同的，并收集了奇点的主要拓扑方面，描述为所涉及的角度的类型和滑动，逃脱和越过区域的位置。同样，提出了这些规范形式的一个参数分叉，并获得了拓扑等效的平滑矢量场。
In this paper we obtain 32 canonical forms for 3D piecewise smooth vector fields presenting the so called cusp-fold singularity. All these canonical forms are topologically distinct and collect the main topological aspects of the singularities described as kind of the tangencies involved and positions of the sliding, escaping and crossing regions. Also, one-parameter bifurcations of these canonical forms are presented and the topologically equivalent piecewise smooth vector fields are obtained.
