Stokes Phenomenon and Differential Galois Groups

Abstract

We will first sketch the contents of this chapter. Let (δ−A be a matrix differential equation over C({z}). Then there is a unique (up to isomorphism over C({z})) quasi-split equation δ−B that is isomorphic, over C((z)), to δ−A (cf. Proposition 3.41). This means that there is a $\hat{F} \notin G{L_n}\left( {C\left( {(z)} \right)} \right)$ such that ${\hat{F}^{{ - 1}}}\left( {\delta - A} \right)\hat{F} = \delta - B$. In the following, δ−A, δ−B, and $\hat{F}$ are fixed and the eigenvalues of δ−A, δ−B are denoted by q₁,…, q _s .