Painlevé III: A Case Study in the Geometry of Meromorphic Connections

The first monograph on Painlevé equations to treat both classical local aspects and modern global aspects simultaneously

Introduces a new method in the study of Painlevé equations, combining local analysis and global topology

Gives a new classification of real solutions of the Third Painlevé equation in terms of their zeros and poles

Inhalt

1. Introduction.- 2.- The Riemann-Hilbert correspondence for P3D6 bundles.- 3. (Ir)Reducibility.- 4. Isomonodromic families.- 5. Useful formulae: three 2 × 2 matrices.- 6. P3D6-TEP bundles.- 7. P3D6-TEJPA bundles and moduli spaces of their monodromy tuples.- 8. Normal forms of P3D6-TEJPA bundles and their moduli spaces.- 9. Generalities on the Painleve´ equations.- 10. Solutions of the Painleve´ equation PIII (0, 0, 4, 4).- 13. Comparison with the setting of Its, Novokshenov, and Niles.- 12. Asymptotics of all solutions near 0.- ...Bibliography. Index.