Ecalle's averages, Rota-Baxter algebras and the construction of moulds
Abstract
Rota-Baxter algebras and Atkinson's method are powerful tools for the factorization of characters on Hopf algebras. The theory of real resummation discovered by J. Ecalle and known as well-behaved averages theory can be reformulated in terms of character factorization. The aim of this article is to explain how Atkinson recursion provides an alternative way to retrieve characters already discovered by Ecalle.
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