Linearization of Nambu structures

Nambu structures are a generalization of Poisson structures in Hamiltonian dynamics, and it has been shown recently by several authors that, outside s ingular points, these structures are locally an exterior product of commuti ng vector fields. Nambu structures also give rise to co-Nambu differential forms, which are a natural generalization of integrable 1-forms to higher o rders. This work is devoted to the study of Nambu tensors and co-Nambu form s near singular points. In particular, we give a classification of linear N ambu structures (integral finite-dimensional Nambu-Lie algebras), and a lin earization of Nambu tensors and co-Nambu forms, under the nondegeneracy con dition.