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

2003/06/12 by M. Mazzocco, Marta Mazzocco, Mazzocco, M.
Chemistry · Mathematics · Physics and Astronomy · #32G34 (Primary) #34M55 #35R99 #53D45 (Secondary) #Advanced Topics in Algebra #Complex Variables (math.CV) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #math.CV #msc:32G34 #msc:34M55 #msc:35R99 #msc:53D45 #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0306020

17 pages

arxiv created 2003/06/12 · openalex publication_date 2003/06/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Note on the Singularity Reduction of Isomonodromy Systems Associated with Garnier Systems
• Isomonodromic deformation of the linear differential system in the Birkhoff standard form
• The geometry of the classical solutions of the Garnier systems
• Description of generalized isomonodromic deformations of rank two linear differential equations using apparent singularities
• Studies on the Garnier system in two variables