Some reductions of rank 2 and genera 2 and 3 Hitchin systems

Abstract: Certain reductions of the rank 2, genera 2 and 3 Hitchin systems are considered, which are shown to give an integrable system of 2, resp. 3, interacting points on the line. It is shown that the reduced systems are particular cases of a certain universal integrable system related to the Lagrange interpolation polynomial. Admissibility of the reduction is proved using computer technique. The corresponding codes are given in the text.