The paper is inspired by the recently formulated belief (cf. also
Bender, Carl M.; Jones, Hugh F., Quantum counterpart of
spontaneously broken classical $\scr{PT}$ symmetry. J. Phys. A 44
(2011), 015301, MR2749106) that the presence of the Kato's
exceptional points in the quantum spectra of energies (i.e., in
physical terms, the emergence of quantum instabilities) finds
certain characteristic parallels (e.g., chaotic behavior) in the
limiting case of the classical system. The present authors decided
to replace the popular unsolvable models by an exactly solvable one.
Their results confirm the current conjecture that the classical
analogue of the exceptional point might be the point of the loss of
the periodicity of the classical complex trajectories.

MR2748864 Sinha, A.; Dutta, D.; Roy, P. Study of classical
mechanical systems with complex potentials. Phys. Lett. A 375
(2011), no. 3, 452--457. 81Qxx