2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/218858We notice 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 a singular behaviour associated with restructuring of classical trajectories. The system with the crypto-Hermitian Hamiltonian H = (p^2+z^2)/2 -igz^5 and hyper-ellictic classical dynamics is studied in details. Analogies with supersymmetric Yang-Mills dynamics are elucidated.References added. Final version to be published in J. Phys. AMathematical PhysicsHigh Energy Physics - TheoryQuantum Physicstext