Painlevé III: A Case Study in the Geometry of Meromorphic Connections 2017 Edition Contributor(s): Guest, Martin A. (Author), Hertling, Claus (Author) |
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ISBN: 3319665251 ISBN-13: 9783319665252 Publisher: Springer OUR PRICE: $42.74 Product Type: Paperback Published: October 2017 |
Additional Information |
BISAC Categories: - Mathematics | Differential Equations - General - Mathematics | Geometry - Algebraic - Mathematics | Mathematical Analysis |
Dewey: 515.352 |
Series: Lecture Notes in Mathematics |
Physical Information: 0.46" H x 6.14" W x 9.21" (0.69 lbs) 204 pages |
Descriptions, Reviews, Etc. |
Publisher Description: The purpose of this monograph is two-fold: it introduces a conceptual language for the geometrical objects underlying Painlev equations, and it offers new results on a particular Painlev 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. As an application, a new global picture o0 is given. |