Exceptional points in quantum and classical dynamics

We note that when a quantum system involves exceptional points, i.e. the special values of parameters where the Hamiltonian loses its self-adjointness and acquires the Jordan block structure, the corresponding classical system also exhibits singular behaviour associated with the restructuring of classical trajectories. A system with the crypto-Hermitian Hamiltonian H = (p(2) + z(2))/2-igz(5) and hyper-elliptic classical dynamics is studied in detail. Analogies with supersymmetric Yang-Mills dynamics are elucidated.