  We study classically the problem of two relativistic particles with an
invariant Duffing-like potential which reduces to the usual Duffing form in the
nonrelativistic limit. We use a special relativistic generalization (RGEM) of
the geometric method (GEM) developed for the analysis of nonrelativistic
Hamiltonian systems to study the local stability of a relativistic Duffing
oscillator. Poincar'e plots of the simulated motion are consistent with the
RGEM. We found a threshold for the external driving force required for chaotic
behavior in the Minkowski spacetime.
