On integrable system on $S^2$ with the second integral quartic in the momenta

Abstract

We consider integrable system on the sphere $S^2$ with an additional integral of fourth order in the momenta. At the special values of parameters this system coincides with the Kowalevski-Goryachev-Chaplygin system.

LaTeX, 6 pages

References in corpus (4)

• Poisson maps and integrable deformations of Kowalevski top
• The Kowalewski top: a new Lax representation
• On a family of integrable systems on $S^2$ with a cubic integral of motion
• On integrable deformations of the spherical top

Cited by in corpus (5)

• Reduction of superintegrable systems: the anisotropic harmonic oscillator
• On natural Poisson bivectors on the sphere
• On bi-integrable natural Hamiltonian systems on the Riemannian manifolds
• On a class of integrable systems with a quartic first integral
• Cubic and Quartic integrals for geodesic flow on 2-torus via system of Hydrodynamic type