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We review the formulation of the problem of electromagnetic self-interaction of a relativistic charged particle in the framework of the manifestly covariant classical mechanics of Stueckeleberg, Horwitz, and Piron. The gauge fields of this theory, in general, cause the mass of the particle to change. We study the four dynamical off-mass-shell orbit equations which result from the expansion of Green's function in the Lorentz force equation for the self-interaction. It appears that there is an attractor in this system which stabilizes the motion of therelativistic charged electron. The attractor may acquire fractal characteristics in the presence of an external field and thus become a strangeattractor

Simulation of the Radiation Reaction Orbits of a Classical Relativistic Charged Particle with Generalized Off-Shell Lorentz Force