Irregular isomonodromic deformations for Garnier systems and Okamoto's canonical transformations
Abstract
In this paper we describe the Garnier systems as isomonodromic deformation equations of a linear system with a simple pole at zero and a Poincaré rank two singularity at infinity. We discuss the extension of Okamoto's birational canonical transformations to the Garnier systems in more than one variable and to the Schlesinger systems.