Painlevé III: A Case Study in the Geometry of Meromorphic Connections
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...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing
2017, 2017
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| Edition: | 1st ed. 2017 |
| Series: | Lecture Notes in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 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