SIGMA 10 (2014), 050, 24 pages      arXiv:1207.4023      https://doi.org/10.3842/SIGMA.2014.050

Geometric Aspects of the Painlevé Equations PIII(D₆) and PIII(D₇)

Marius van der Put and Jaap Top
Johann Bernoulli Institute, University of Groningen, P.O. Box 407, 9700 AK Groningen, The Netherlands

Received October 15, 2013, in final form April 10, 2014; Published online April 23, 2014

Abstract
The Riemann-Hilbert approach for the equations PIII(D₆) and PIII(D₇) is studied in detail, involving moduli spaces for connections and monodromy data, Okamoto-Painlevé varieties, the Painlevé property, special solutions and explicit Bäcklund transformations.

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

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