On a class of integrable systems with a quartic first integral

Galliano Valent (1, 2)

1 CPT - E2 Géométrie, Physique et Symétries
2 CPT - Centre de Physique Théorique - UMR 7332

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 details and leads to a class of models living on the manifolds S^2, H^2 or R^2. As special cases we recover Kovalevskaya's integrable system and a generalization of it due to Goryachev.

Domaines: Physique mathématique [math-ph]

Galliano Valent. On a class of integrable systems with a quartic first integral. Regular and Chaotic Dynamics, 2013, 18 (04), pp.394-424. ⟨10.1134/S1560354713040060⟩. ⟨hal-01224293⟩