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… (More)
We present algorithms which involve both the splitting of formal series solutions to linear ordinary differential equations with polynomial coefficients into a finite sum of subseries which themselves will be solutions of linear ODEs, and the simplification of the recurrence relations satisfied by their coefficients.When coping with series that are… (More)
We exhibit an internal coproduct on the Hopf algebra of finite topologies recently defined by the second author, C. Malvenuto and F. Patras, dual to the composition of " quasi-ormoulds " , which are the natural version of J. Ecalle's moulds in this setting. All these results are displayed in the linear species formalism.