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

• Κύριοι συγγραφείς: Guest, Martin A. (Συγγραφέας), Hertling, Claus (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Σειρά: Lecture Notes in Mathematics, 2198
• Θέματα: Mathematics.; Algebraic geometry.; Functions of complex variables.; Differential equations.; Special functions.; Ordinary Differential Equations.; Algebraic Geometry.; Special Functions.; Functions of a Complex Variable.

The purpose of this monograph is two-fold:  it introduces a conceptual language for the geometrical objects underlying Painlevé equations,  and it offers new results on a particular Painlevé III equation of type  PIII (D6), called PIII (0, 0, 4, −4), describing its relation to isomonodromic families...

Πίνακας περιεχομένων:

• 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.