Escapes in Hamiltonian systems with multiple exit channels: Part II

TL;DR

This paper investigates escape dynamics in open Hamiltonian systems with multiple escape channels, analyzing how initial conditions influence escape times and basin structures through extensive numerical simulations.

Contribution

It extends previous work by systematically studying the influence of different perturbations on escape basins and times in systems with multiple escape channels.

Findings

Regions of non-escaping motion coexist with escape basins.

Longer escape periods occur near fractal basin boundaries.

Lower escape rates are found within the basins of escape.

Abstract

We explore the escape dynamics in open Hamiltonian systems with multiple channels of escape continuing the work initiated in Part I. A thorough numerical investigation is conducted distinguishing between trapped (ordered and chaotic) and escaping orbits. The determination of the location of the basins of escape towards the different escape channels and their correlations with the corresponding escape periods of the orbits is undoubtedly an issue of paramount importance. We consider four different cases depending on the perturbation function which controls the number of escape channels on the configuration space. In every case, we computed extensive samples of orbits in both the configuration and the phase space by numerically integrating the equations of motion as well as the variational equations. It was found that in all examined cases regions of non-escaping motion coexist with several basins of escape. The larger escape periods have been measured for orbits with initial conditions in the vicinity of the fractal structure, while the lowest escape rates belong to orbits with initial conditions inside the basins of escape. In addition, we related the model potential with applications in the field of reactive multichannel scattering. We hope that our numerical analysis will be useful for a further understanding of the escape mechanism of orbits in open Hamiltonian systems with two degrees of freedom.