[Réduction supplémentaire des formes normales d'applications différentiables]
La réduction supplémentaire des formes normales classiques d'applications formelle est étudiée dans cette note. En utilisant des formules récursives pour le calcul de l'application obtenue par une transformation formelle tangente à l'identité, nous développons la notion de formes normales d'ordre N et d'ordre infini pour les applications formelles, et nous donnons des conditions suffisantes pour l'unicité de ces formes normales.
Further reduction for classical normal forms of formal maps is considered in this note. Based on a recursive formula for computing the transformed map of a formal map under a near identity formal transformation, we develop the concepts of Nth order normal forms and infinite order normal forms for formal maps, and give some sufficient conditions for uniqueness of normal forms of formal maps.
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@article{CRMATH_2006__343_10_657_0,
author = {Wang, Duo and Zheng, Min and Peng, Jianping},
title = {Further reduction of normal forms of formal maps},
journal = {Comptes Rendus. Math\'ematique},
pages = {657--660},
publisher = {Elsevier},
volume = {343},
number = {10},
year = {2006},
doi = {10.1016/j.crma.2006.10.005},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2006.10.005/}
}
TY - JOUR AU - Wang, Duo AU - Zheng, Min AU - Peng, Jianping TI - Further reduction of normal forms of formal maps JO - Comptes Rendus. Mathématique PY - 2006 SP - 657 EP - 660 VL - 343 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.10.005/ DO - 10.1016/j.crma.2006.10.005 LA - en ID - CRMATH_2006__343_10_657_0 ER -
%0 Journal Article %A Wang, Duo %A Zheng, Min %A Peng, Jianping %T Further reduction of normal forms of formal maps %J Comptes Rendus. Mathématique %D 2006 %P 657-660 %V 343 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2006.10.005/ %R 10.1016/j.crma.2006.10.005 %G en %F CRMATH_2006__343_10_657_0
Wang, Duo; Zheng, Min; Peng, Jianping. Further reduction of normal forms of formal maps. Comptes Rendus. Mathématique, Tome 343 (2006) no. 10, pp. 657-660. doi : 10.1016/j.crma.2006.10.005. http://www.numdam.org/articles/10.1016/j.crma.2006.10.005/
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