On linear differential equations with reductive Galois group

Galois Theory of Linear Differential Equations

Galois Theory of Linear Differential Equations - ReadingSample

Computing the differential Galois group of a one-parameter family of second order linear differential equations

We develop algorithms to compute the differential Galois group corresponding to a one-parameter family of second order homogeneous ordinary linear differential equations with rational function coefficients. More precisely, we consider equations of the form ∂2Y ∂x2 + r1 ∂Y ∂x + r2Y = 0, where r1,r2 ∈C(x, t) and C is an algebraically closed field of characteristic zero. We work in the setting of ...

1 Introduction to the Galois Theory of Linear Differential Equations

This paper is an expanded version of the 10 lectures I gave as the 2006 London Mathematical Society Invited Lecture Series at the Heriot-Watt University, 31 July 4 August 2006†. My goal was to give the audience an introduction to the algebraic, analytic and algorithmic aspects of the Galois theory of linear differential equations by focusing on some of the main ideas and philosophies and on exa...

Lie symmetries and differential Galois groups of linear equations

For a linear ordinary differential equation the Lie algebra of its infinitesimal Lie symmetries is compared with its differential Galois group. For this purpose an algebraic formulation of Lie symmetries is developed. It turns out that there is no direct relation between the two above objects. In connection with this a new algorithm for computing the Lie symmetries of a linear ordinary differen...