Isomonodromic deformation of the linear differential system in the Birkhoff standard form

TL;DR

This paper discusses the construction of isomonodromic deformations for linear meromorphic systems in Birkhoff standard form, focusing on the unique challenges posed by resonant irregular singularities at infinity.

Contribution

It analyzes Bolibruch's method for isomonodromic deformation in systems with resonant irregular singularities, highlighting its special characteristics.

Findings

Characterization of isomonodromic deformations in Birkhoff form

Analysis of resonant irregular singularity effects

Discussion of Bolibruch's construction method

Abstract

We consider a linear meromorphic system in the Birkhoff standard form. The construction of the isomonodromic deformation of it proposed by Bolibruch is discussed. This construction has some special characteristics because of resonant irregular singularity at the infinity.