Escape dynamics in a Hamiltonian system with four exit channels

TL;DR

This study investigates how orbits escape in a four-channel Hamiltonian system, analyzing the influence of energy levels and initial conditions on escape rates and basin structures using numerical methods.

Contribution

It provides a detailed numerical analysis of escape mechanisms, basin structures, and fractality in a four-channel Hamiltonian system, extending previous research.

Findings

Escape rate decreases as energy increases.

Escape basins are fractal near the escape energy.

Orbits near basin boundaries escape faster.

Abstract

We reveal the escape mechanism of orbits in a Hamiltonian system with four exit channels composed of two-dimensional perturbed harmonic oscillators. We distinguish between trapped chaotic, non-escaping regular and escaping orbits by conducting a thorough and systematic numerical investigation in both the configuration and the phase space. We locate the different basins of escape and we relate them withe the corresponding escape times of orbits. The SALI method is used for determining the ordered or chaotic nature of the orbits. It was observed that trapped and non-escaping orbits coexist with several escape basins. When the energy is very close to the escape energy the escape rate of orbits is huge, while as the value of the energy increases the orbits escape more quickly to infinity. Furthermore, initial conditions of orbits located near the boundaries of the basins of escape and also in the vicinity of the fractal domains were found to posses the largest escape rates. The degree of the fractality of the phase space was calculated as a function of the value of the energy. Our results were compared with earlier related work.