ON THE HOLONOMIC DEFORMATION OF LINEAR DIFFERENTIAL EQUATIONS WITH A REGULAR SINGULAR POINT AND AN IRREGULAR SINGULAR POINT

For each positive integer g, we derive a completely integrable Hamiltonian system in g variables from the holonomic deformation of a linear differential equation with a regular singular point and an irregular singular point of Poincare rank $ g + 1 $. For $ g = 1 $, this Hamiltonian system is equivalent to the fourth Painleve equation