Abstract
Some years ago Moshé Flato pointed out that it would be interesting to develop Nambu's idea to generalize Hamiltonian mechanics. An interesting new formalism in that direction was proposed by L. Takhtajan. His theory gave new perspectives concerning deformation quantization, and many authors have developed its mathematical features. The purpose of this Letter is to show that this theory, at first dedicated to physics, presents a new point of view for the study of singularities of integrable 1-forms. Namely, we will prove that any integrable 1-form which vanishes at a point and has a nonzero linear part at this point is, up to multiplication by a nonvanishing function, the formal pull-back of a two-dimensional 1-form. We also obtain a classification of quadratic integrable 1-forms.
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