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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 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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