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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2512.04471 |
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| author | Borin, Daniel Rando, Danilo S. Leonel, Edson D. Oliveira, Diego F. M. |
| author_facet | Borin, Daniel Rando, Danilo S. Leonel, Edson D. Oliveira, Diego F. M. |
| contents | 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 ($K = K_c$), the dynamics reduce to a normal form that produces a power-law decay $d(n) \propto n^{-1/2}$, 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 $d_n = d_0 e^{-n/τ}$ for $K < K_c$, with $τ\propto (K_c - K)^{-1}$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04471 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence Dynamics and Scaling Laws in the Dissipative Relativistic Kicked Rotator Borin, Daniel Rando, Danilo S. Leonel, Edson D. Oliveira, Diego F. M. Chaotic Dynamics 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 ($K = K_c$), the dynamics reduce to a normal form that produces a power-law decay $d(n) \propto n^{-1/2}$, 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 $d_n = d_0 e^{-n/τ}$ for $K < K_c$, with $τ\propto (K_c - K)^{-1}$, 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. |
| title | Convergence Dynamics and Scaling Laws in the Dissipative Relativistic Kicked Rotator |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2512.04471 |