Explicit integration of a generic Hénon-Heiles system with quartic potential
Source of Publication
Journal of Nonlinear Mathematical Physics
© 2017 the authors. 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.
Sottocornola, Nicola, "Explicit integration of a generic Hénon-Heiles system with quartic potential" (2017). Scopus Indexed Articles. 1309.