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We study the electromagnetic two-body problem of classical electrodynamics as a prototype dynamical system with state-dependent delays. The equations of motion are analysed with reference to motion along a straight line in the presence of an electrostatic field. We consider the general electromagnetic equations of motion for point charges with advanced and retarded interactions and study two limits (a) retarded-only interactions (Dirac electrodynamics) and (b) half-retarded plus halfadvanceddoi:10.1088/1751-8113/43/20/205103 fatcat:2ls6aa67g5fuxpkizvo332novy