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For a complex Lie group $G$ with a real form $G_0\subset G$, we prove thatany Hamiltionian automorphism $\phi$ of a coadjoint orbit $\mathcal O_0$ of$G_0$ whose connected components are simply connected, may be approximated byholomorphic $\mathcal O_0$-invariant symplectic automorphism of thecorresponding coadjoint orbit of $G$ in the sense of Carleman, provided that$\mathcal O$ is closed. In the course of the proof, we establish theHamiltonian density property for closed coadjoint orbits of all complex Liegroups.

Hamiltonian Carleman approximation and the density property for coadjoint orbits