2026/02/24 by L. Salasnich, F. Sattin · 1 voice
Physics and Astronomy · #Chaos control and synchronization #Chaotic #Chaotic scattering #Dynamical billiards #Exponential function #Hamiltonian (control theory) #Hamiltonian system #Multiplicative function #Parametric statistics #Quantum chaos and dynamical systems #Trajectory #nlin.CD #stochastic dynamics and bifurcation
paper · pdf · doi:10.1016/j.chaos.2026.118259
arxiv published 2026/02/24 · openalex created_date 2026/03/01 · arxiv updated 2026/03/17 · openalex publication_date 2026/03/18 · openalex updated_date 2026/07/28
In this work we revisit the geometric approach to chaos in Hamiltonian dynamics, by means of the Jacobi-Levi-Civita equation (JLCE). We inspect numerically two low-dimensional dynamical systems; show that, along chaotic orbits, the exponential divergence between nearby trajectories quantified by the JLCE does not unfold in a continuous manner, rather is closer to a multiplicative discrete process: in correspondence of each turning point, where the trajectory bounces away from the boundary of the energetically allowed region, the relative separation increases sharply and abruptly. We highlight through analytical and numerical arguments that the chaotic rather than regular nature of the trajectory is determined by the details of the scattering with the boundary, and interpret these results in terms of parametric resonance theory, and specifically the Mathieu equation.