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

An overview of the escape dynamics in the Hénon–Heiles Hamiltonian system 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Meccanica Springer Journals

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

Meccanica , Volume 52 (12) – Mar 3, 2017
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Publisher
Springer Netherlands
Copyright
Copyright © 2017 by Springer Science+Business Media Dordrecht
Subject
Physics; Classical Mechanics; Civil Engineering; Automotive Engineering; Mechanical Engineering
ISSN
0025-6455
eISSN
1572-9648
D.O.I.
10.1007/s11012-017-0647-8
Publisher site
See Article on Publisher Site

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.

Journal

MeccanicaSpringer Journals

Published: Mar 3, 2017

References

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