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This article is cited in 10 scientific papers (total in 10 papers)
On a Class of Integrable Systems with a Quartic First Integral
Galliano Valentabc a Laboratoire de Physique Théorique et des Hautes Energies, Unité associée au CNRS UMR 7589, 2 Place Jussieu, 75251 Paris Cedex 05, France
b Aix-Marseille Université, CNRS, CPT, UMR 7332, 13288 Marseille, France
c Université de Toulon, CNRS, CPT, UMR 7332, 83957 La Garde, France
Abstract:
We generalize, to some extent, the results on integrable geodesic flows on two dimensional manifolds with a quartic first integral in the framework laid down by Selivanova and Hadeler. The local structure is first determined by a direct integration of the differential system which expresses the conservation of the quartic observable and is seen to involve a finite number of parameters. The global structure is studied in some detail and leads to a class of models on the manifolds $\mathbb{S}^2$, $\mathbb{H}^2$ or $\mathbb{R}^2$. As special cases we recover Kovalevskaya’s integrable system and a generalization of it due to Goryachev.
Keywords:
integrable Hamiltonian systems, quartic polynomial integral, manifolds for Riemannian metrics.
Received: 22.04.2013 Accepted: 28.06.2013
Citation:
Galliano Valent, “On a Class of Integrable Systems with a Quartic First Integral”, Regul. Chaotic Dyn., 18:4 (2013), 394–424
Linking options:
https://www.mathnet.ru/eng/rcd120 https://www.mathnet.ru/eng/rcd/v18/i4/p394
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Abstract page: | 111 | References: | 27 |
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