Sp. Drake et al., CHAOS IN SPECIAL RELATIVISTIC DYNAMICS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 53(2), 1996, pp. 1351-1361
The study of chaos in relativistic systems (both special and general)
is a newly emergent held. The main focus of this paper is the study of
the chaotic trajectories of a charged particle in a static electric f
ield. The full special relativistic equations of motion are used. Here
we concentrate on motion in a field that is produced by two fixed cen
ters with equal charge. The chaotic nature of these trajectories is in
vestigated by examining the fractal nature of the attractor basin boun
dary. An examination of how these properties change with respect to fu
ndamental 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 dynami
cs.