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Let (M, ω, H) be an hamiltonian system endowed with a finite dimensional space A of first integrals. The center of A for the Poisson bracket defines an infinitesimal hamiltonian action of R k on M. If O is a compact orbit of this action, we give a necessary and sufficient condition (involving the principal parts of functions in A at a point of O) for the system to admit a normal form of 'toric...