TO ESCAPE OR NOT TO ESCAPE, THAT IS THE QUESTION — PERTURBING THE HÉNON–HEILES HAMILTONIAN

Abstract

In this work, we study the Hénon–Heiles Hamiltonian, as a paradigm of open Hamiltonian systems, in the presence of different kinds of perturbations as dissipation, noise and periodic forcing, which are very typical in different physical situations. We focus our work on both the effects of these perturbations on the escaping dynamics and on the basins associated to the phase space and to the physical space. We have also found, in presence of a periodic forcing, an exponential-like decay law for the survival probability of the particles in the scattering region where the frequency of the forcing plays a crucial role. In the bounded regions, the use of the OFLI2 chaos indicator has allowed us to characterize the orbits. We have compared these results with the previous ones obtained for the dissipative and noisy case. Finally, we expect this work to be useful for a better understanding of the escapes in open Hamiltonian systems in the presence of different kinds of perturbations.