About the Trimmed and the Poincare-Dulac normal form of diffeomorphisms

Jacky Cresson (1) , Jasmin Raissy (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 PISA-TONELLI - Dipartimento di matematica "L. Tonelli" .

We study two particular continuous prenormal forms as defined by Jean Ecalle and Bruno Vallet for local analytic diffeomorphism: the Trimmed form and the Poincare-Dulac normal form. We first give a self-contain introduction to the mould formalism of Jean Ecalle. We provide a dictionary between moulds and the classical Lie algebraic formalism using non-commutative formal power series. We then give full proofs and details for results announced by J. Ecalle and B. Vallet about the Trimmed form of diffeomorphisms. We then discuss a mould approach to the classical Poincare-Dulac normal form of diffeomorphisms. We discuss the universal character of moulds taking place in normalization problems.

Mots clés: normal forms; continuous prenormal forms; mould calculus; diffeomorphisms

Domaines: Systèmes dynamiques [math.DS]

Jacky Cresson, Jasmin Raissy. About the Trimmed and the Poincare-Dulac normal form of diffeomorphisms. 2006. ⟨hal-00076843⟩