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| FIELD | Math: CMC |
|---|---|
| DATE | April 19 (Thu), 2018 |
| TIME | 16:00-18:00 |
| PLACE | 1423 |
| SPEAKER | Nguyen Tien Zung |
| HOST | Kim, Sung Yeon |
| INSTITUTE | Universit Toulouse |
| TITLE | Convergence versus integrability in normal form |
| ABSTRACT | 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 ? la Poincar?-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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