We investigate the emergence of chaos, bifurcation phenomena, and fractal phase-space structures in a high-energy relativistic Hamiltonian system subject to a periodically kicked electromagnetic field. The model is based on a modified relativistic dispersion relation incorporating Planck-scale corrections, leading to a nonlinear stroboscopic map that generalizes the classical kicked-rotor dynamics. By analyzing bifurcation diagrams and maximal Lyapunov exponents over a broad range of control parameters, we demonstrate that relativistic effects profoundly reshape the route to chaos. In particular, the presence of velocity saturation suppresses unbounded phase-space stretching, resulting in delayed bifurcations, truncated period-doubling cascades, and saturation of Lyapunov exponents even in strongly chaotic regimes. The system exhibits a rich mixed phase space characterized by the coexistence of chaotic seas, stable islands, cantori, and fractal basin boundaries, with transport properties that differ qualitatively from their nonrelativistic counterparts. Our results show that increasing the drift parameter enhances chaotic transport, while stronger relativistic corrections stabilize motion and preserve hierarchical phase-space organization. These findings highlight the fundamental role of modified dispersion relations in constraining instability and shaping chaos at high energy, providing new insights into nonlinear dynamics in relativistic and quantum-gravity-inspired systems.
El-Nabulsi et al. (Tue,) studied this question.