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Nonlinear Sciences > Chaotic Dynamics

arXiv:1709.04360 (nlin)
[Submitted on 11 Sep 2017 (v1), last revised 14 Sep 2017 (this version, v2)]

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

Authors:Euaggelos E. Zotos
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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.
Comments: 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
Subjects: Chaotic Dynamics (nlin.CD)
Cite as: arXiv:1709.04360 [nlin.CD]
  (or arXiv:1709.04360v2 [nlin.CD] for this version)
  https://doi.org/10.48550/arXiv.1709.04360
Journal reference: Meccanica, vol. 52, pp. 2615-2630 (2017)
Related DOI: https://doi.org/10.1007/s11012-017-0647-8

Submission history

From: Euaggelos E. Zotos [view email]
[v1] Mon, 11 Sep 2017 10:22:12 UTC (4,945 KB)
[v2] Thu, 14 Sep 2017 05:49:09 UTC (4,945 KB)
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