Ecalle's arborification-coarborification transforms and Connes-Kreimer Hopf algebra
Dynamical Systems
2014-06-03 v2 Combinatorics
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.
Keywords
Cite
@article{arxiv.1212.4740,
title = {Ecalle's arborification-coarborification transforms and Connes-Kreimer Hopf algebra},
author = {Frédéric Fauvet and Frederic Menous},
journal= {arXiv preprint arXiv:1212.4740},
year = {2014}
}