SEPARATION OF VARIABLES FOR SOME SYSTEMS WITH A FOURTH-ORDER INTEGRAL OF MOTION

摘要

We construct separation variables for Yehia's integrable deformations of the Kovalevskaya top and the Chaplygin system on a sphere. In the general case, the corresponding quadratures are given by the Abel- Jacobi map on a two-dimensional submanifold of the Jacobian of a genus-three algebraic curve, which is not hyperelliptic.