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Comptes Rendus Mathématique
Volume 347, n° 19-20
pages 1129-1134 (octobre 2009)
Doi : 10.1016/j.crma.2009.07.009
Received : 25 November 2008 ;  accepted : 6 July 2009
Théorème de Poincaré–Lyapunov et conditions nécessaires d’existence d’un centre
About the Poincaré–Lyapunov theorem and necessary conditions for the existence of a center
 

Driss Boularas
Xlim, UMR 6090, DMI, FST, université de Limoges, 123, avenue A. Thomas, 87060 Limoges, France 

Résumé

Posé au XIXème siècle par Lyapunov et Poincaré, le problème du « centre–foyer » n’a été résolu que pour des cas particuliers. Dans cette Note, grâce à une présentation matricielle et sans passer aux coordonnées polaires, on « revisite » le théorème de Poincaré–Lyapunov et on décrit une méthode « directe » de calcul des conditions d’existence d’un centre pour une famille de systèmes différentiels. Pour citer cet article : D. Boularas, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

The full text of this article is available in PDF format.
Abstract

Since the end of the XIX century, the “center–focus” problem interested many people. However, up to now, it was solved only for particular families of differential systems. In this Note, with the help of a new matricial presentation, we re-visit the Poincaré–Lyapunov theorem and we give a “direct” computational method of the conditions of a center for some differential systems. To cite this article: D. Boularas, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

The full text of this article is available in PDF format.


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