Volume 24, Issue 3, June 2017, Pages 346 - 355
Explicit integration of a generic Hénon-Heiles system with quartic potential
Authors
Nicola Sottocornola
Department of Mathematics and Statistics, Zayed University, Abu Dhabi, UAE,nicola.spinelli@zu.uc.ae
Received 28 February 2017, Accepted 30 March 2017, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2017.1341697How to use a DOI?
- Keywords
- Integrable systems; separation of coordinates; Hénon-Heiles systems
- Abstract
There are seven time independent, integrable, Hénon-Heiles systems: three with cubic and four with quartic potential. The cubic and one of the quartic cases have been separated in the last decades. The other three cases 1:6:1, 1:6:8 and 1:12:16 have resisted several attempts in the last years. In this paper we focus our attention on the 1:12:16 case whose equations of motion have been separated only in the degenerate case ab = 0. We give here the separation coordinates for the generic case using a method introduced by Franco Magri in 2005 under the name of Kowalevski’s Conditions.
- Copyright
- © 2017 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Nicola Sottocornola PY - 2021 DA - 2021/01/06 TI - Explicit integration of a generic Hénon-Heiles system with quartic potential JO - Journal of Nonlinear Mathematical Physics SP - 346 EP - 355 VL - 24 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2017.1341697 DO - 10.1080/14029251.2017.1341697 ID - Sottocornola2021 ER -