2025/07/08 by Anne Kétri P. da Fonseca, da Fonseca, Anne Kétri P., Diego F. M. Oliveira +3
Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Quantum chaos and dynamical systems #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2507.06395
openalex publication_date 2025/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigated the unbounded diffusion observed in a time-dependent oval-shaped billiard and its suppression owing to inelastic collisions with the boundary. The main focus is on the behavior of the diffusion coefficient, which plays a key role in describing the scaling invariance characteristic of this transition. For short times, the low-action regime is characterized by a constant diffusion coefficient, which begins to decay after a crossover iteration, thereby suppressing the unlimited growth of velocity. We demonstrate that this behavior is scaling-invariant concerning the control parameters and can be described by a homogeneous generalized function and its associated scaling laws. The critical exponents are determined both phenomenologically and analytically, including the decay exponent beta = -1, previously identified in the diffusion coefficient of the dissipative standard map.