| Dewey Class |
515.352 |
| Title |
Painlevé III: A Case Study in the Geometry of Meromorphic Connections ([EBook]) / by Martin A. Guest, Claus Hertling. |
| Author |
Guest, Martin A. |
| Added Personal Name |
Hertling, Claus |
| Other name(s) |
SpringerLink (Online resource) |
| Publication |
Cham : Springer International Publishing AG , 2017 |
| Physical Details |
XII, 204 pages: 12 illus. : online resource. |
| Series |
Lecture Notes in Mathematics ; 2198 0075-8434 ; |
| ISBN |
978-3-319-66526-9 |
| Summary Note |
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 of vector bundles on P1 with meromorphic connections. This equation is equivalent to the radial sine (or sinh) Gordon equation and, as such, it appears widely in geometry and physics. It is used here as a very concrete and classical illustration of the modern theory of vector bundles with meromorphic connections. Complex multi-valued solutions on C* are the natural context for most of the monograph, but in the last four chapters real solutions on R>0 (with or without singularities) are addressed. These provide examples of variations of TERP structures, which are related to tt∗ geometry and harmonic bundles. As an application, a new global picture of 0 is given.(cit. from the Introduction of the book): |
| Contents note |
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. |
| Mode of acces to digital resource |
Digital book.- Cham : Springer International Publishing AG, 2017. - Mode of access : World Wide Web. - System requirements : Internet Explorer 6.0 (or higher) of Firefox 2.0 (or higher). Available as searchable text in PDF format. or ePub format |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) |
| Internet Site |
https://doi.org/10.1007/978-3-319-66526-9 |
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