Isomonodromy for the Degenerate Fifth Painlevé Equation

[摘要] This is a sequel to papers by the last two authors making the Riemann-Hilbert correspondence and isomonodromy explicit. For the degenerate fifth Painlevé equation, the moduli spaces for connections and for monodromy are explicitly computed. It is proven that the extended Riemann-Hilbert morphism is an isomorphism. As a consequence these equations have the Painlevé property and the Okamoto-Painlevé space is identified with a moduli space of connections. Using MAPLE computations, one obtains formulas for the degenerate fifth Painlevé equation, for the Bäcklund transformations.

[关键词] moduli space for linear connections;irregular singularities;Stokes matrices;monodromy spaces;isomonodromic deformations;Painlev´e equations