Cyclicity of composition operators on the Fock space

In this paper we provide a full characterization of cyclic composition operators defined on the d-dimensional Fock space $\mathcal F(\mathbb C^d)$ in terms of their symbol. Also, we study the supercyclicity and convex-cyclicity of this type of operators. We end this work by computing the approximation numbers of compact composition operators defined on $\mathcal F(\mathbb C^d)$.