Many classical integrable systems (like the Euler, Lagrange and Kowalewski tops or the Neumann system) as well as finite dimensional reductions of many integrable PDEs share the property of being algebraically completely integrable systems4. This means that they are completely integrable Hamiltonian systems in the usual sense and, moreover, their complexified invariant tori are open subsets of complex Abelian tori on which the complexified flow is linear. To such systems the powerful algebro-geometrical techniques may be applied.
