Free dense subgroups of holomorphic automorphisms

We show the existence of free dense subgroups, generated by two elements, in the holomorphic shear and overshear group of complex-Euclidean space and extend this result to the group of holomorphic automorphisms of Stein manifolds with the density property, provided there exists a generalized translation. The conjugation operator associated to this generalized translation is hypercyclic on the topological space of holomorphic automorphisms.