Résumé : In this PhD thesis are studied the polylogarithms and the harmonic sums at non-positive (i.e., weakly negative) multi-indices. General results about these objects in relation with Hopf algebras are pr ovided. The technics exploited here are based on the combinatorics of noncommmutative generating series relative to the Hopf phi-huffle algebra. Our work will also propose a global process to renormalize divergent polyzetas. Finally, we will apply these ideas to non-linear dynamical systems with singular inputs.
The jury will be composed of: Gérard Duchamp, Hoang Ngoc Minh (directeurs), Sylvie Paycha, Dominique Manchon (rapporteurs), Karol Penson, Vincent Rivasseau, Loic Foissy, Christophe Tollu.
|Dernière modification : Wednesday 07 December 2016||Contact : Cyril.Banderier at lipn.univ-paris13.fr|