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Real Abelian manifolds and the top of Kowalewski. (Variétes abéliennes réelles et toupie de Kowalewski.) (French) Zbl 0774.58012
From the authors’ abstract: “The authors describe, in a very didactic and complete work, how are the common levels of the first integrals in the nonsymmetrical top of Sofya Kowalevskaya. They show how the real aspects of the spectral curve method yield the study of the corresponding Liouville tori. They also say that this was already done by Kharlamov, based on studies of Appelrot, with tedious computations and arguments not completely detailed”.

MSC:
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
14K25 Theta functions and abelian varieties
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References:
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