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Normal Forms for Two Classes of Exact Poisson Structures in Dimension Four
Author(s) -
Cruz I.,
Mena-Matos H.
Publication year - 2006
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610705022532
Subject(s) - poisson distribution , mathematics , dimension (graph theory) , divergence (linguistics) , singular point of a curve , manifold (fluid mechanics) , mathematical analysis , pure mathematics , point (geometry) , discrete poisson equation , geometry , uniqueness theorem for poisson's equation , statistics , mechanical engineering , philosophy , linguistics , uniqueness , engineering
We consider singular exact Poisson structures on an oriented manifold of dimension 4. Using normal forms for divergence‐free vector fields on R 3 and for 1‐parameter deformations of functions on R 3 we produce normal forms for two classes of such Poisson structures around the singular point.