An overview of the escape dynamics in the Henon-Heiles Hamiltonian system

TL;DR

This paper systematically investigates escape dynamics in the Henon-Heiles Hamiltonian system, analyzing trapped and escaping orbits across various energy levels and phase space slices, and relating escape basins to escape times.

Contribution

It provides a comprehensive numerical analysis of escape basins, escape times, and the chaotic nature of orbits in the Henon-Heiles system, extending previous studies with detailed phase space exploration.

Findings

Regions of non-escaping orbits coexist with escape basins.

Escape basins are related to escape periods of orbits.

Chaotic and regular trapped motions are distinguished using SALI.

Abstract

The aim of this work is to revise but also explore even further the escape dynamics in the H\'{e}non-Heiles system. In particular, we conduct a thorough and systematic numerical investigation distinguishing between trapped (ordered and chaotic) and escaping orbits, considering only unbounded motion for several energy levels. It is of particular interest, to locate the basins of escape towards the different escape channels and relate them with the corresponding escape periods of the orbits. In order to elucidate the escape process we conduct a thorough investigation in several types of two-dimensional planes and also in a three-dimensional subspace of the entire four-dimensional phase space. We classify extensive samples of orbits by integrating numerically the equations of motion as well as the variational equations. In an attempt to determine the regular or chaotic nature of trapped motion, we apply the SALI method, as an accurate chaos detector. It was found, that in all studied cases regions of non-escaping orbits coexist with several basins of escape. Most of the current outcomes have been compared with previous related work.