Geodesic
Integrable systems on the sphere associated with genus three algebraic curves
Russian journal of nonlinear dynamics, Tome 7 (2011) no. 1, pp. 53-74

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New variables of separation for few integrable systems on the two-dimensional sphere with higher order integrals of motion are considered in detail.We explicitly describe canonical transformations of initial physical variables to the variables of separation and vice versa, calculate the corresponding quadratures and discuss some possible integrable deformations of initial systems.
Keywords: integrable systems; separation of variables; Abel equations. 
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     title = {Integrable systems on the sphere associated with genus three algebraic curves},
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V. A. Khudobakhshov; A. V. Tsiganov. Integrable systems on the sphere associated with genus three algebraic curves. Russian journal of nonlinear dynamics, Tome 7 (2011) no. 1, pp. 53-74. http://geodesic.mathdoc.fr/item/ND_2011_7_1_a2/