Galois Theory of Parameterized Differential Equations and Linear Differential Algebraic Groups

2005/02/18 by Phyllis J. Cassidy, Cassidy, Phyllis J., Michael F. Singer +1
Mathematics · #12H05 #12H20 #34M50 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:12H05 #msc:12H20 #msc:34M50

paper · pdf · doi:10.48550/arxiv.math/0502396

arxiv created 2005/02/18 · arxiv updated 2009/12/01

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.

Related

• Computing the differential Galois group of a one-parameter family of\n second order linear differential equations
• Difference Galois theory of linear differential equations
• Root Parametrized Differential Equations for the classical groups
• Algebraic groups as difference Galois groups of linear differential equations
• New classes of parameterized differential Galois groups