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FIELD Math: CMC April 19 (Thu), 2018 16:00-18:00 1423 Nguyen Tien Zung Kim, Sung Yeon Universit Toulouse Convergence versus integrability in normal form I'll explain the following theorem: any local real analytic or holomorphic vector field, which is integrable with the help of Darboux-type first integrals (these are functions of the type \$\prod_i G_i^{c_i}\$ where the \$c_i\$ are complex numbers and the \$G_i\$ are local analytic functions) and meromorphic commuting vector fields admits a local analytic normalization à la Poincaré-Birkhoff. The proof of this result is based on a geometric method involving associated torus actions of dynamical systems, geometric approximations, and a holomorphic extension lemma. This talk is based on a series of 3 papers of mine on the subject (Math Research Letters 2002, Annals Math 2005, and preprint 2018).

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