The symplectic structure of rational Lax pair systems

Abstract

We consider dynamical systems associated to Lax pairs depending rationnally on a spectral parameter. We show that we can express the symplectic form in terms of algebro--geometric data provided that the symplectic structure on L is of Kirillov type. In particular, in this case the dynamical system is integrable.

8 pages, no figure, Latex

References in corpus (1)

• The symplectic structure of the spin Calogero model

Cited by in corpus (3)

• Riemann surfaces, separation of variables and classical and quantum integrability
• On the Quantum Inverse Problem for the Closed Toda Chain
• Riemann bilinear form and Poisson structure in Hitchin-type systems