BIHAMILTONIAN SYSTEMS IN ODD DIMENSION

This article is devoted to the study of the global geometry of dynamic al systems of a special kind, the bihamiltonian systems defined on a c losed and odd dimensional manifold M. The dynamics of such a system is linked to the dynamics of a follation A which is characterised by cer tain properties along the leaves (existence of an affine structure) an d transverse to the leaves (transverse rigidity due to the existence o f a connection). The analysis of these properties leads us to general results in odd dimension. Namely one can prove that the manifold M is a fibration whose fibers are the closures of the leaves of A. Then one can apply these results to obtain a very precise description in dimen sions 3 and 5. (C) Elsevier, Paris.