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JOURNALS // Russian Journal of Nonlinear Dynamics // Archive

Nelin. Dinam., 2011 Volume 7, Number 1, Pages 53–74 (Mi nd208)

Integrable systems on the sphere associated with genus three algebraic curves

V. A. Khudobakhshov, A. V. Tsiganov

St.-Petersburg State University

Abstract: 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.

UDC: 532.5

MSC: 70H20; 70H06; 37K10

Received: 14.03.2011
Revised: 27.03.2011



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