Galois Theory of Parameterized Differential Equations and Linear Differential Algebraic Groups
Classical Analysis and ODEs
2007-05-23 v1
Abstract
We present a Galois theory of parameterized linear differential equations where the Galois groups are linear differential algebraic groups, that is, groups of matrices whose entries are functions of the parameters and satisfy a set of differential equations with respect to these parameters. We present the basic constructions and results, give examples, discuss how isomonodromic families fit into this theory and show how results from the theory of linear differential algebraic groups may be used to classify systems of second order linear differential equations.
Keywords
Cite
@article{arxiv.math/0502396,
title = {Galois Theory of Parameterized Differential Equations and Linear Differential Algebraic Groups},
author = {Phyllis J. Cassidy and Michael F. Singer},
journal= {arXiv preprint arXiv:math/0502396},
year = {2007}
}