Geodesic
Separation of variables for some systems with a fourth-order integral of motion
Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 3, pp. 468-481 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: bi-Hamiltonian geometry, separation of variables, Kovalevskaya top. 
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Yu. A. Grigor'ev; V. A. Khudobakhshov; A. V. Tsiganov. Separation of variables for some systems with a fourth-order integral of motion. Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 3, pp. 468-481. http://geodesic.mathdoc.fr/item/TMF_2013_177_3_a3/

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