La variété caractéristique d'un système différentiel analytique
Annales de l'Institut Fourier, Volume 50 (2000) no. 2, p. 491-518

The characteristic variety of an analytic linear differential system has the two following classical properties:

1. Independance of the filtration.

2. Integrability (e.g. stability by Poisson bracket).

Here, it is proven that the first property is still true for non-linear systems outside of the zero-section. The second property is still true generically (at the other points, the question remains open).

La variété caractéristique d’un système différentiel linéaire analytique possède les deux propriétés classiques suivantes :

1. Indépendance de la filtration.

2. Intégrabilité (i.e. stabilité par crochet de Poisson).

On montre ici que la première propriété reste vraie hors de la section nulle pour les systèmes non linéaires. La seconde propriété reste vraie génériquement (ailleurs, la question reste ouverte).

@article{AIF_2000__50_2_491_0,
     author = {Malgrange, Bernard},
     title = {La vari\'et\'e caract\'eristique d'un syst\`eme diff\'erentiel analytique},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {50},
     number = {2},
     year = {2000},
     pages = {491-518},
     doi = {10.5802/aif.1763},
     zbl = {0951.35007},
     mrnumber = {2001m:32020},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_2000__50_2_491_0}
}
Malgrange, Bernard. La variété caractéristique d'un système différentiel analytique. Annales de l'Institut Fourier, Volume 50 (2000) no. 2, pp. 491-518. doi : 10.5802/aif.1763. http://www.numdam.org/item/AIF_2000__50_2_491_0/

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