Geometric Aspects of the Painlevé Equations $\mathrm{PIII}({\mathrm{D}}_6)$ and $\mathrm{PIII}({\mathrm{D}}_7)$

Abstract

The Riemann-Hilbert approach for the equations $\mathrm{PIII}({\mathrm{D}}_6)$ and $\mathrm{PIII}({\mathrm{D}}_7)$ is studied in detail, involving moduli spaces for connections and monodromy data, Okamoto-Painlevé varieties, the Painlevé property, special solutions and explicit Bäcklund transformations.

References in corpus (5)

• Moduli of Stable Parabolic Connections, Riemann-Hilbert correspondence and Geometry of Painlevé equation of type VI, Part I
• Moduli of unramified irregular singular parabolic connections on a smooth projective curve
• Painlevé equations and deformations of rational surfaces with rational double points
• Moduli spaces for linear differential equations and the Painlevé equations
• A Riemann--Hilbert approach to Painlevé IV

Cited by in corpus (4)

• Isomonodromy for the Degenerate Fifth Painlevé Equation
• The Painlevé III equation of type (0,0,4,-4), its associated vector bundles with isomonodromic connections, and the geometry of the movable poles
• The Stokes Phenomenon and Some Applications
• Moduli Spaces for the Fifth Painlevé Equation