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Article Dans Une Revue Annales Scientifiques de l'École Normale Supérieure Année : 2017

Ecalle's arborification-coarborification transforms and Connes-Kreimer Hopf algebra

Résumé

We give a natural and complete description of Ecalle's mould-comould formalism within a Hopf-algebraic framework. The arborification transform thus appears as a factorization of characters, involving the shuffle or quasishuffle Hopf algebras, thanks to a universal property satisfied by Connes-Kreimer Hopf algebra. We give a straightforward characterization of the fundamental process of homogeneous coarborification, using the explicit duality between decorated Connes-Kreimer and Grossman-Larson algebras. Finally, we introduce a new Hopf algebra that systematically underlies the calculations for the normalization of local dynamical systems.
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Dates et versions

hal-00767373 , version 1 (19-12-2012)
hal-00767373 , version 2 (02-06-2014)

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Citer

Frédéric Fauvet, Frederic Menous. Ecalle's arborification-coarborification transforms and Connes-Kreimer Hopf algebra. Annales Scientifiques de l'École Normale Supérieure, 2017, 50 (1), pp.39-83. ⟨10.24033/asens.2315⟩. ⟨hal-00767373v2⟩
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