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NORMAL FORMS FOR TWO CLASSES OF EXACT POISSON STRUCTURES IN DIMENSION FOUR

Published online by Cambridge University Press:  22 February 2006

I. CRUZ  and
H. MENA-MATOS
I. CRUZ
Affiliation:
Centro de Matemática da Universidade do Porto, Departamento de Matemática Aplicada, Faculdade de Ciências da Universidade do Porto, Campo Alegre, 687,4169-007 Porto, Portugalimcruz@fc.up.pt
H. MENA-MATOS
Affiliation:
Centro de Matemática da Universidade do Porto, Departamento de Matemática Aplicada, Faculdade de Ciências da Universidade do Porto, Campo Alegre, 687,4169-007 Porto, Portugalmmmatos@fc.up.pt
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Abstract

We consider singular exact Poisson structures on an oriented manifold of dimension 4. Using normal forms for divergence-free vector fields on ${\mathbb R}^3$ and for 1-parameter deformations of functions on ${\mathbb R}^3$ we produce normal forms for two classes of such Poisson structures around the singular point.

Keywords

53D1758K50
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 73 , Issue 1 , February 2006 , pp. 194 - 208
Copyright
The London Mathematical Society 2006

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Footnotes

Financial support from FEDER (approved by FCT - POCTI/MAT/36528/99)