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Comptes Rendus Mathématique
Volume 346, n° 15-16
pages 829-832 (août 2008)
Doi : 10.1016/j.crma.2008.07.007
Received : 29 May 2008 ;  accepted : 3 July 2008
Sectorial normalization of Poisson structures
Normalisation sectorielle de structures de Poisson
 

Philipp Lohrmann
Universität Zürich, Institut für Mathematik, Winterthurerstr. 190, CH-8057 Zürich, Switzerland 

Abstract

Our study deals with some singular Poisson structures holomorphic near   admitting a polynomial normal form, i.e. a finite number of formal invariants. Their normalizing series generally diverge. We show the existence of normalizing transformations holomorphic on some sectorial domains  , where   denotes a monomial associated to the problem. It follows an analytic classification. To cite this article: P. Lohrmann, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

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Résumé

Notre étude porte sur une catégorie de structures de Poisson singulières holomorphes au voisinage de   et admettant une forme normale formelle polynomiale i.e. un nombre fini dʼinvariants formels. Les séries normalisantes sont divergentes en général. On montre lʼexistence de transformations normalisantes holomorphes sur des domaines sectoriels de la forme  , où   est un monôme associé au problème. Il sʼensuit une classification analytique. Pour citer cet article : P. Lohrmann, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

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


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