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

Abstract

The aim of this work is to revise but also explore even further the escape dynamics in the Hénon-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.

arXiv commentPublished in Meccanica journal. arXiv admin note: Previous papers with related context: arXiv:1511.04908, arXiv:1511.04889, arXiv:1505.03847, arXiv:1609.00681, arXiv:1706.07298, arXiv:1604.04613, arXiv:1411.4864, arXiv:1508.05198, arXiv:1505.03968, arXiv:1604.04622

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• Geometry of escape and transition dynamics in the presence of dissipative and gyroscopic forces in two degree of freedom systems
• Probabilistic description of dissipative chaotic scattering
• Fractal signatures of non-Kerr spacetimes in the shadow of light-ring bifurcations