Fouad Zinoun

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The aim of this paper is to show the role of first integrals in further reducing the normal form unfolding of Hamiltonian systems. Based on a work by Cicogna and Gaeta, the joint normal form approach for Hamiltonian vector fields is considered. This normal form procedure, couched in a Lie-Poincaré scheme, allows us to see that we can reduce simultaneously(More)
An improved version of the well-known Poincaré-Dulac’s normal form theorem is first proposed. It is shown that, for a nonlinear vector field, a normal form near a singular point can always be chosen so that the number of nonlinear components is at most equal to the number of Jordan blocks in the normalized leading matrix, thus leading to the “simplest” form(More)
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