On the nonintegrability of the Stark-Zeeman Hamiltonian system (Q1969097)

This paper studies the nonintegrability in the Liouvillian sense of the Stark-Zeeman Hamiltonian. Since the authors consider the cases where the famous Ziglin theorem does not work, they present a proof of the nonintegrability of the Stark-Zeeman Hamiltonian. In particular, they generalize the result of \textit{M. P. Kummer} and \textit{A. W. Saenz} [Commun. Math. Phys. 162, 447-465 (1994; Zbl 0817.58016)] about the non-integrability of the pure Zeeman Hamiltonian. The authors' proof is based on differential Galois theory.