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1 Statement of the result Consider the second order linear differential equation fl=ry, withrc Q(z). Let Qc~ denote the algebraic closure of the field of rational numbers Q and let G denote thedifferential Galois group over Qcl(z) of this equation. Then G C S/(2, Qct). F~r any solution y # O of the equation the element u = $ satisfies the Riccati equation… (More)
a r t i c l e i n f o a b s t r a c t The notion of strict equivalence for order one differential equations of the form f (y , y, z) = 0 with coefficients in a finite extension K of C(z) is introduced. The equation gives rise to a curve X over K and a derivation D on its function field K (X). Procedures are described for testing strict equivalence, strict… (More)
We survey some constructive aspects of dierential Galois theory and indicate some analogies between ordinary Galois theory and dier-ential Galois theory in characteristic zero and nonzero.
Multisummation provides a transparent description of Stokes matrices which is reviewed here together with some applications. Examples of moduli spaces for Stokes matrices are computed and discussed. A moduli space for a third Painlevé equation is made explicit. It is shown that the monodromy identity, relating the topological monodromy and Stokes matrices,… (More)