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New examples of systems of the Kowalevski type. (English) Zbl 1309.37052

Summary: A new examples of integrable dynamical systems are constructed. An integration procedure leading to genus two theta-functions is presented. It is based on a recent notion of discriminantly separable polynomials. They have appeared in a recent reconsideration of the celebrated Kowalevski top, and their role here is analogue to the situation with the classical Kowalevski integration procedure.

MSC:

37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
34A34 Nonlinear ordinary differential equations and systems
70E40 Integrable cases of motion in rigid body dynamics
70E17 Motion of a rigid body with a fixed point
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