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The methods of [vdP-Sa, vdP1, vdP2] are applied to the fourth Painlevé equation. One obtains a Riemann– Hilbert correspondence between moduli spaces of rank two connections on P 1 and moduli spaces for the mon-odromy data. The moduli spaces for these connections are identified with Okamoto–Painlevé varieties and the Painlevé property follows. For an(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)
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)