Irregular isomonodromic deformations for Garnier systems and Okamoto's canonical transformations

The paper describes the Garnier systems as isomonodromic deformation equations of a linear system with a simple pole at 0 and a Poincaré rank 1 singularity at infinity. The extension of Okamoto's birational canonical transformations to the Garnier systems in more than one variable and to the Schlesinger systems is discussed.