Normal forms and bifurcations of vector fields

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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: