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Normalisation holomorphe de structures de Poisson

Published online by Cambridge University Press:  17 July 2009

PHILIPP LOHRMANN
PHILIPP LOHRMANN*
Affiliation:
Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland (email: philipp.lohrmann@math.uzh.ch)
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Abstract

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We show that a Poisson structure whose linear part vanishes can be holomorphically normalized in a neighbourhood of its singular point $0\in \Bbb C^n$ if, on the one hand, a Diophantine condition on a Lie algebra associated to the quadratic part is satisfied and, on the other hand, the normal form satisfies some formal conditions.

Résumé

Nous montrons qu’une structure de Poisson à 1-jet nul est holomorphiquement conjuguée vers une forme normale au sens de Dufour–Wade, au voisinage de son point singulier $0\in \Bbb C^n$, si sont vérifiées d’une part une condition diophantienne sur une algèbre de Lie associée à la partie quadratique, d’autre part certaines conditions sur la forme normale formelle.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 4 , August 2010 , pp. 1165 - 1199
Copyright
Copyright © Cambridge University Press 2009

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