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arXiv · 1212.4740

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

Frédéric Fauvet·Frederic Menous
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Abstract

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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Frédéric Fauvet, Frederic Menous. 2012-12-19. Ecalle's arborification-coarborification transforms and Connes-Kreimer Hopf algebra. https://arxiv.org/abs/1212.4740

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