Chaos in special relativistic dynamics

The study of chaos in relativistic systems (both special and general) is a newly emergent field. The main focus of this paper is the study of the chaotic trajectories of a charged particle in a static electric field. The full special relativistic equations of motion are used. Here we concentrate on motion in a field that is produced by two fixed centers with equal charge. The chaotic nature of these trajectories is investigated by examining the fractal nature of the attractor basin boundary. An examination of how these properties change with respect to fundamental parameters of the problem, such as charges, mass, and charge separation, is undertaken. We emphasize that fractal basin boundaries provide an important characterization of chaos in relativistic dynamics.