Fast and slow escapes in forced chaotic scattering: The Newtonian and the relativistic regimes

We study chaotic scattering phenomena in the paradigmatic Hénon-Heiles Hamiltonian when a rotating external force is applied. This analysis builds on and extends our previous work on the relativistic unperturbed case and the classical case with equal forcing terms affecting the equations of motion. In this more realistic scenario with a rotating external forcing, we compare the results obtained in the classical energy regime with those in the relativistic regime. Our comparison focuses on the analysis of the exit basins, as well as resonant and trapping phenomena, which correspond to fast and slow escape times, respectively. In addition to the dependence on the particle energy E, we also investigate the system's behavior at both low and high perturbing frequencies ω. Notably, when the particles are in the relativistic regime, we observe a shift in the evolution of the resonant frequency as a function of both E and ω.