Some applications of the parameterized Picard-Vessiot theory

TL;DR

This paper explores applications of the parameterized Picard-Vessiot theory to ordinary differential equations, focusing on aspects related to monodromy, and provides insights into its theoretical implications.

Contribution

It demonstrates new applications of parameterized Picard-Vessiot theory in understanding monodromy in differential equations.

Findings

Enhanced understanding of monodromy via parameterized Picard-Vessiot theory

Connections established between differential Galois groups and monodromy

Potential new methods for analyzing differential equations

Abstract

This expository paper presents some applications of the parameterized Picard-Vessiot theory for ordinary differential equations, mainly related to monodromy.