PT -symmetric classical mechanics

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