%0 Journal Article
%T On a class of integrable systems with a quartic first integral
%A Galliano Valent
%J Physics
%D 2013
%I arXiv
%R 10.1134/S1560354713040060
%X 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.
%U http://arxiv.org/abs/1304.5859v1