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

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.