Year: 2026
Type: article
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 ( $$K = K_\textrm{c}$$ K = K c ), the dynamics reduce to a normal form that produces a power-law decay $$d(n) \propto n^{-1/2}$$ d ( n ) ∝ n - 1 / 2 , from which the critical exponents $$\alpha = 1$$ α = 1 , $$\beta = -1/2$$ β = - 1 / 2 , and $$z = -2$$ z = - 2 are derived. These analytical predictions are confirmed numerically and shown to satisfy the homogeneous scaling relation $$z = \alpha / \beta$$ z = α / β . Linearization of the map near the fixed point yields an exponential relaxation law $$d_n = d_0 e^{-n/\tau }$$ d n = d 0 e - n / τ for $$K < K_\textrm{c}$$ K < K c , with $$\tau \propto (K_\textrm{c} - K)^{-1}$$ τ ∝ ( K c - K ) - 1 , leading to the relaxation exponent $$\delta = -1$$ 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.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,790
OpenAlex ID: W7155746204