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Matrix Lax polynomials, geometry of Prym varieties and systems of Hess-Appel’rot type. (English) Zbl 1122.37043
Summary: We consider a four-dimensional generalization of Hess-Appel’rot system and costruct its Lax pair. Both classical and algebro-geometric integration procedure are proceeded. The algebro-geometric integration is based on deep facts from geometry of Prym varieties such as the Mumford relation and Mumford-Dalalyan theory. The integration is similar to the integration of Lagrange bitop which has recetly been performed by the authors.

37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
14H40 Jacobians, Prym varieties
70E40 Integrable cases of motion in rigid body dynamics
70G55 Algebraic geometry methods for problems in mechanics
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