Résumé : For a complex Lie group $G$ with a real form $G_0\subset G$, we prove that any Hamiltionian automorphism $\varphi$ of a coadjoint orbit ${\mathcal{O}}_0$ of $G_0$ whose connected components are simply connected, may be approximated by holomorphic $O_0$-invariant symplectic automorphism of the corresponding coadjoint orbit of $G$ in the sense of Carleman, provided that $\mathcal{O}$ is closed. In the course of the proof, we establish the Hamiltonian density property for closed coadjoint orbits of all complex Lie groups.

Keywords : Carleman approximation; co-adjoint orbits; Andersén-Lempert theorem