Jacobians of singularized spectral curves and completely integrable systems
نویسنده
چکیده
We state two recent results concerning the linearization of integrable systems on generalised Jacobians. Then we apply this to the (complexified) spherical pendulum.
منابع مشابه
A Lie Theoretic Galois Theory for the Spectral Curves of an Integrable System. Ii
In the study of integrable systems of ODE’s arising from a Lax pair with a parameter, the constants of the motion occur as spectral curves. Many of these systems are algebraically completely integrable in that they linearize on the Jacobian of a spectral curve. In an earlier paper the authors gave a classification of the spectral curves in terms of the Weyl group and arranged the spectral curve...
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M P = {A(x) ∈ M : det(A(x)− yIr) = P (x, y)}. The system (1) has an obvious symmetry group G = IPGLr(I C; J) which is the subgroup of the projective group IPGLr(I C) formed by matrices which commute with J . The group G acts on M by conjugation, the action is Poisson, and the reduced Hamiltonian system is completely integrable too. As the symmetry group G acts freely and properly on the general...
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