简单切族及其包络的Perestroika
Simple tangential families and perestroikas of their envelopes
摘要：
切向族是从平滑曲线切向发出的单参数射线族。我们分类切族芽左右等价：我们证明了有两个无穷级数和四个零星的简单奇异的切族芽（除了两个稳定的奇点）。我们给出了它们的标准形和极小切向变形（即，变形之间的切向家庭），我们描述了相应的信封perestroikas的小余维。我们还讨论了非简单切向族的包络奇点。
英文摘要：
Tangential families are 1-parameter families of rays emanating tangentially from smooth curves. We classify tangential family germs up to Left-Right equivalence: we prove that there are two infinite series and four sporadic simple singularities of tangential family germs (in addition to two stable singularities). We give their normal forms and miniversal tangential deformations (i.e., deformations among tangential families), and we describe the corresponding envelope perestroikas of small codimension. We also discuss envelope singularities of non simple tangential families.
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