On the non-integrability of quartic potentials (Q1383421)
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scientific article; zbMATH DE number 1139510
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the non-integrability of quartic potentials |
scientific article; zbMATH DE number 1139510 |
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On the non-integrability of quartic potentials (English)
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15 February 1999
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The integrability or non-integrability (in the sense of Liouville) of the Hamiltonian mechanical system corresponding to the Hénon-Heiles potential is known in the literature [see, for example, \textit{S. L. Ziglin}, Funct. Anal. Appl. 16, 181-189 (1983); translation from Funkts. Anal. Prilozh. 16, No. 3, 30-41 (1982; Zbl 0524.58015) and Funct. Anal. Appl. 17, 6-17 (1983; Zbl 0518.58016); \textit{H. Ito}, Kodai Math. J. 8, 120-138 (1985; Zbl 0577.58016)]. The aim of this paper is the study of the (non-)integrability of a quartic generalization of the Hénon-Heiles potential by using the Ziglin theorem.
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Hénon-Heiles system
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non-integrability of Hamiltonian systems
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Ziglin theorem
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