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The Kowalewski top 99 years later: a Lax pair, generalizations and explicit solutions. (English) Zbl 0819.58013
Summary: A “natural” Lax pair for the Kowalewski top is derived by using a general group-theoretic approach. This gives a new insight into the algebraic geometry of the top and leads to its complete solution via finite-band integration theory.

MSC:
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
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
70E15 Free motion of a rigid body
70H05 Hamilton’s equations
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References:
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