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

Abstract

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 Poincaré rank g + 1. For g = 1, this Hamiltonian system is equivalent to the fourth Painlevé equation.