Spectral curve and Hamiltonian structure of isomonodromic SU(2) Calogero-Gaudin system

This paper presents an approach to the Hamiltonian structure of isomonodromic systems of matrix ODE’s on a torus from their spectral curve. An isomonodromic analogue of the so called SU(2) Calogero-Gaudin system is used for a case study of this approach. A clue of this approach is a mapping from the Lax equation to a dynamical system of a finite number of points on the spectral curve. The coordinates of these moving points give a new set of canonical variables, which have been used in the literature for separation of variables of many integrable systems including the usual SU(2) Calogero-Gaudin system itself. The same machinery turns out to work for the isomonodromic system on a trous, though the separability is lost and the non-autonomous nature of the system causes technical complications. Strong evidence is shown which suggests that this isomonodromic system is equivalent to a previously known isomonodromic system of second order scalar ODE’s on a torus. arXiv nlin.SI/0111019