Apparent singularities of Fuchsian equations, and the Painlev\'e VI equation and Garnier systems

TL;DR

This paper investigates the movable singularities of Garnier systems by exploring their connection with Fuchsian systems' isomonodromic deformations, addressing inverse monodromy problems and their implications.

Contribution

It provides new insights into the singularity structure of Garnier systems and advances understanding of inverse monodromy problems related to Fuchsian equations.

Findings

Characterization of movable singularities in Garnier systems

Connection between Garnier systems and Fuchsian isomonodromic deformations

Results on existence of solutions for inverse monodromy problems

Abstract

We study movable singularities of Garnier systems using the connection of the latter with isomonodromic deformations of Fuchsian systems. Questions on the existence of solutions for some inverse monodromy problems are also considered.