2026/02/19 by Edson D. Leonel, Mayla A. M. de Almeida, Juan Pedro Tarigo +2 · 1 voice
Physics and Astronomy · #nlin.CD
paper · pdf · doi:10.1103/7231-j7zv
We present a comprehensive discussion of a transition from integrability to non-integrability in an oval billiard with a static boundary. This transition is controlled by a deformation parameter ε, which modifies the boundary shape from circular, corresponding to ε=0 and an integrable dynamics, to oval for ε≠ 0, where non-integrability emerges. The deformation of the circular billiard gives rise to a chaotic layer that develops along a well-defined stripe in phase space. By introducing a set of transformations that isolate this chaotic stripe, we characterise the diffusive spreading of ensembles of trajectories and identify an observable, ω_rms,\rm sat, which plays the role of an order parameter for the transition. For small deformations, the saturation value of the diffusion obeys the scaling law ω_rms,\rm sat∝εα, with a critical exponent α=0.507(2), vanishing continuously as ε→ 0. The associated susceptibility, χ=dω_rms,\rm sat/dε, diverges in the same limit, signalling the presence of critical behavior analogous to that observed in second-order (continuous) phase transitions in statistical mechanics.