Abstract
In this paper, after some recalls about Poisson cohomology, we first study what the general method is in order to obtain a bi-Hamiltonian formulation of a given Hamiltonian system by means of a deformation. Then we show that the bi-Hamiltonian formulation which results from the deformation of a Poisson structure by means of a suitable non-Noether symmetry cannot explain the complete integrability for a large class of Arnold–Liouville integrable systems; next we prove that the deformation must be made in this context by a suitable mastersymmetry. At last, we give several examples.
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