Difference Galois theory of linear differential equations

σ-Galois theory of linear difference equations

Inspired by the numerous applications of the differential algebraic independence results from [36], we develop a Galois theory with an action of an endomorphism σ for systems of linear difference equations of the form φ(y) = Ay , where A ∈ GLn(K ) and K is a φσ-field, that is, a field with two given commuting endomorphisms φ and σ, like in Example 2.1. This provides a technique to test whether ...

Galois Theory of Linear Differential Equations

Galois Theory of Linear Differential Equations - ReadingSample

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...

Introduction to the Galois Theory of Linear Ordinary Differential Equations

We define the differential Galois group of a linear homogeneous ordinary differential equation and illustrate the type of information about solutions packaged within. The initial format is classical; at the end we indicate how the results can be conceptualized geometrically.