PT-Symmetric Classical Mechanics

This paper reports the results of an ongoing in-depth analysis of the classical trajectories of the class of non-Hermitian PT -symmetric Hamiltonians H = p+x(ix) (ε ≥ 0). A variety of phenomena, heretofore overlooked, have been discovered such as the existence of infinitely many separatrix trajectories, sequences of critical initial values associated with limiting classical orbits, regions of broken PT -symmetric classical trajectories, and a remarkable topological transition at ε = 2. This investigation is a work in progress and it is not complete; many features of complex trajectories are still under study.