Isomonodromy for the degenerate fifth Painlevé equation

Abstract

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.