About the Trimmed and the Poincare-Dulac normal form of diffeomorphisms
Dynamical Systems
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/0605716,
title = {About the Trimmed and the Poincare-Dulac normal form of diffeomorphisms},
author = {Jacky Cresson and Jasmin Raissy},
journal= {arXiv preprint arXiv:math/0605716},
year = {2007}
}
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27 pages