Existence of completely elliptic periodic orbits of symmetric and convex Hamiltonians

Using certain quadratic forms associated to symplectic endomorphisms which we compare with the Clarke-Ekeland dual action functional, we prove, THEOREM. - Let H be a C-2-Hamiltonian defined on R-2n, strictly convex, proper and invariant under a certain symplectic rational positive and non-degenerate rotation (this is defined in the introduction); then, every hypersurface of H contains a completely elliptic periodic orbit. This generalizes the result of G. Dell'Antonio, B. D 'Onofrio and I. Ekeland contained in [1]. (C) Academie des Sciences/Elsevier, Paris.