### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 029, 14 pages      arXiv:1612.03674      https://doi.org/10.3842/SIGMA.2017.029

### Isomonodromy for the Degenerate Fifth Painlevé Equation

Primitivo B. Acosta-Humánez a, Marius van der Put b and Jaap Top b
a) Universidad Simón Bolívar, Barranquilla, Colombia
b) University of Groningen, Groningen, The Netherlands

Received December 12, 2016, in final form May 01, 2017; Published online May 09, 2017

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.

Key words: moduli space for linear connections; irregular singularities; Stokes matrices; monodromy spaces; isomonodromic deformations; Painlevé equations.

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