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.

References in corpus (3)

• Painlevé monodromy manifolds, decorated character varieties and cluster algebras
• Moduli spaces for linear differential equations and the Painlevé equations
• A Riemann--Hilbert approach to Painlevé IV

Cited by in corpus (2)

• Variations for Some Painlevé Equations
• Moduli Spaces for the Fifth Painlevé Equation