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math.DS2025
Explicit linearization of multi-dimensional germs and vector fields through Ecalle's tree expansions
Frédéric Fauvet, Frédéric Menous, David Sauzin
We revisit the Siegel linearization problem by means of explicit formulas of non-recursive type for the linearizing transformations of a non-resonant holomorphic germ of diffeomorp…
math.DS2012
Ecalle's arborification-coarborification transforms and Connes-Kreimer Hopf algebra
Frédéric Fauvet, Frederic Menous
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 ch…