An overview of the escape dynamics in the Hénon–Heiles Hamiltonian system

2017/03/03 by Euaggelos E. Zotos · 15 citations
Physics and Astronomy · #Chaos control and synchronization #Chaotic #Dynamics (music) #Equations of motion #Hamiltonian (control theory) #Hamiltonian system #Motion (physics) #Periodic orbits #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Subspace topology #Work (physics) #nlin.CD

paper · pdf · doi:10.1007/s11012-017-0647-8

published in Meccanica 52(11-12), 2615-2630 (Springer Science+Business Media) · Published 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

openalex publication_date 2017/03/03 · openalex created_date 2017/03/16 · arxiv created 2017/09/14 · arxiv updated 2017/09/28 · openalex updated_date 2026/08/05

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.

Citations

• Escapes in Hamiltonian systems with multiple exit channels: Part II
• Escape dynamics in a Hamiltonian system with four exit channels
• Escapes in Hamiltonian systems with multiple exit channels: Part I
• Fractal basin boundaries and escape dynamics in a multiwell potential
• Elucidating the escape dynamics of the four hill potential
• Fugitive stars in active galaxies
• Revealing the escape mechanism of three-dimensional orbits in a tidally limited star cluster
• Comparing the escape dynamics in tidally limited star cluster models
• Escape dynamics and fractal basin boundaries in Seyfert galaxies
• Escape dynamics in a binary system of interacting galaxies
• Diffusion and scaling in escapes from two-degrees-of-freedom Hamiltonian systems
• Limit of small exits in open Hamiltonian systems