Notes on Non-Generic Isomonodromy Deformations

TL;DR

This paper reviews key results on non-generic isomonodromy deformations of linear differential systems with irregular singularities, emphasizing the distinction between weak and strong deformations and relating them to classical Fuchsian system deformations.

Contribution

It clarifies the concept of weak versus strong isomonodromic deformations in the context of Pfaffian systems, extending classical Fuchsian deformation theory.

Findings

Distinction between weak and strong isomonodromic deformations clarified.

Relation established between non-generic deformations and classical Schlesinger deformations.

Framework provided for analyzing irregular singularities with coalescing eigenvalues.

Abstract

Some of the main results of [Cotti G., Dubrovin B., Guzzetti D., Duke Math. J., to appear, arXiv:1706.04808], concerning non-generic isomonodromy deformations of a certain linear differential system with irregular singularity and coalescing eigenvalues, are reviewed from the point of view of Pfaffian systems, making a distinction between weak and strong isomonodromic deformations. Such distinction has a counterpart in the case of Fuchsian systems, which is well known as Schlesinger and non-Schlesinger deformations, reviewed in Appendix A.