Geodesic
About the Trimmed and the Poincaré-Dulac Normal Form of Diffeomorphisms
Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 1, pp. 55-80.

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. - In this paper, we give a self-contained introduction to the mould formalism of J. Écalle. We provide a dictionary between moulds and the classical Lie algebraic formalism using non-commutative formal power series. We review results by J. Écalle and B. Vallet about the Trimmed form of local analytic diffeomorphisms of $\mathbb{C}^n$, for which we provide full proofs and details. This allows us to discuss a mould approach to the classical Poincaré-Dulac normal form for diffeomorphisms. 
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Cresson, Jacky; Raissy, Jasmin. About the Trimmed and the Poincaré-Dulac Normal Form of Diffeomorphisms. Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 1, pp. 55-80. http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_1_a2/

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