Abstract We investigate the convergence dynamics of this system near period-doubling bifurcations by combining analytical derivations and large-scale numerical simulations. At the bifurcation threshold (K = Kc K = K c), the dynamics reduce to a normal form that produces a power-law decay d (n) n^-1/2 d (n) ∝ n - 1 / 2, from which the critical exponents = 1 α = 1, = -1/2 β = - 1 / 2, and z = -2 z = - 2 are derived. These analytical predictions are confirmed numerically and shown to satisfy the homogeneous scaling relation z = / z = α / β. Linearization of the map near the fixed point yields an exponential relaxation law dₙ = d₀ e^-n/ d n = d 0 e - n / τ for K K K c, with (Kc - K) ^-1 τ ∝ (K c - K) - 1, leading to the relaxation exponent = -1 δ = - 1. The remarkable agreement between theory and simulation demonstrates that the dissipative relativistic kicked rotator shares the same universality class as one-dimensional unimodal maps, despite its higher dimensionality and relativistic corrections.
Borin et al. (Sun,) studied this question.