标题： 通过鞍点奇点的示例介绍模态微积分 显示英文标题

标题： Initiation to mould calculus through the example of saddle-node singularities

摘要： 本文提出对Écalle的模计算的初步介绍，这是一种强大的组合工具，可以为与解析奇点向量场相关的正规化级数提供令人惊讶的显式公式。 这通过鞍点奇点的情况进行说明，这些奇点由二维向量场生成，这些向量场在形式上共轭于欧拉向量场$x^2\frac{\pa}{\pa x}+(x+y)\frac{\pa}{\pa y}$，并且其形式正规化在$1/x$中被证明是恢复的。 显示英文摘要

摘要： This article proposes an initiation to \'Ecalle's mould calculus, a powerful combinatorial tool which yields surprisingly explicit formulas for the normalising series attached to an analytic germ of singular vector field. This is illustrated on the case of saddle-node singularities, generated by two-dimensional vector fields which are formally conjugate to Euler's vector field $x^2\frac{\pa}{\pa x}+(x+y)\frac{\pa}{\pa y}$, and for which the formal normalisation proves to be resurgent in $1/x$.