Normal forms and bifurcations of vector fields

整个项目集中在解析动力学中的基本问题，特别是依赖于参数的低维动力系统：一维微分同胚，平面向量场，实矢量场或复叶面场，以及线性微分系统。动力系统是依赖于时间的系统。要找到给定系统的显式解是非常困难的。庞卡莱是研究和理解动力系统解的几何方法的创始人。这些方法允许得出定性的结论，即使没有明确的解的公式。为了更好地理解动力系统，攻击它们的弱点是很重要的：相空间中的奇点和参数空间中的分岔值。这项研究项目正是围绕这些问题展开的：

The whole project is centered on fundamental problems in analytic dynamics, especially low dimensional dynamical systems depending on parameters: 1-dimensional diffeomorphisms, planar vector fields, either real vector fields or complex foliations, and linear differential systems. Dynamical systems are systems which depend on the time. It is very difficult to find explicit solutions of a given system. Poincaré was the founder of geometric methods to study and understand the solutions of dynamical systems. These methods allow drawing qualitative conclusions, even without having explicit formulas for the solutions. In order to better understand dynamical systems, it is important to attack them at their weak points: the singularities in phase space and the bifurcation values in parameter space. The research project is centered precisely on these matters: