-symmetric classical mechanics

Abstract

This paper reports the results of an ongoing in-depth analysis of the classical trajectories of the class of non-Hermitian -symmetric Hamiltonians H = p2 + x2 (ix) ε (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 -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.