The symplectic holomorphic density property for Calogero-Moser spaces

We introduce the symplectic holomorphic density property and the Hamiltonian holomorphic density property together with the corresponding version of Andersén-Lempert theory. We establish these properties for the Calogero-Moser space ${\mathcal{C}}_n$ of $n$ particles and describe its group of holomorphic symplectic automorphisms.