Comptes Rendus
no. 10
Dynamical Systems
Further reduction of normal forms of formal maps
[Réduction supplémentaire des formes normales d'applications différentiables]

Présenté par : Bernard Malgrange

Duo Wang1 ; Min Zheng1 ; Jianping Peng1
1 LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China
Comptes Rendus. Mathématique, Volume 343 (2006) no. 10, pp. 657-660.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.10.005
Duo Wang 1 ; Min Zheng 1 ; Jianping Peng 1

1 LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China 
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Duo Wang; Min Zheng; Jianping Peng. Further reduction of normal forms of formal maps. Comptes Rendus. Mathématique, Volume 343 (2006) no. 10, pp. 657-660. doi : 10.1016/j.crma.2006.10.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.10.005/

[1] G. Chen; J. Della Dora Normal forms for differential maps near a fixed point, Numerical Algorithms, Volume 22 (1999), pp. 213-230

[2] H. Kokubu; H. Oka; D. Wang Linear grading function and further reduction of normal forms, J. Differential Equations, Volume 132 (1996), pp. 293-318

[3] J. Peng, Further reduction of normal forms and dynamics of a financial model, Ph.D. thesis, School of Mathematical Sciences, Peking University, 2004

[4] D. Wang, M. Zheng, J. Peng, Further reduction of normal forms and unique normal forms of smooth maps, Preprint, 2006

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