Explicit integration of a generic Hénon-Heiles system with quartic potential |
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Authors: | Nicola Sottocornola |
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Institution: | Department of Mathematics and Statistics, Zayed University, Abu Dhabi, UAE |
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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. |
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Keywords: | Integrable systems separation of coordinates Hénon-Heiles systems |
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