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On a class of integrable systems with a quartic first integral

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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 {ie394-1}2, ℍ2 or ℝ2. As special cases we recover Kovalevskaya’s integrable system and a generalization of it due to Goryachev.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique et des Hautes Energies, Unité associée au CNRS UMR 7589, 2 Place Jussieu, 75251, Paris Cedex 05, France

    Galliano Valent

  2. CNRS, CPT, UMR 7332, Aix-Marseille Université, 13288, Marseille, France

    Galliano Valent

  3. CNRS, CPT, UMR 7332, Université de Toulon, 83957, La Garde, France

    Galliano Valent

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  1. Galliano Valent
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Correspondence to Galliano Valent.

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Valent, G. On a class of integrable systems with a quartic first integral. Regul. Chaot. Dyn. 18, 394–424 (2013). https://doi.org/10.1134/S1560354713040060

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  • DOI: https://doi.org/10.1134/S1560354713040060

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