2025/12/04 by Borin, Daniel, Rando, Danilo S., Leonel, Edson D. +1
#Chaotic Dynamics (nlin.CD) #FOS: Physical sciences
paper · doi:10.48550/arxiv.2512.04471
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), the dynamics reduce to a normal form that produces a power-law decay d(n) ∝ n-1/2, from which the critical exponents α= 1, β= -1/2, and z = -2 are derived. These analytical predictions are confirmed numerically and shown to satisfy the homogeneous scaling relation z = α/ β. Linearization of the map near the fixed point yields an exponential relaxation law dn = d0 e-n/τ for K < Kc, with τ∝ (Kc - K)-1, leading to the relaxation exponent 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.