Name: Painlevé Iii: A Case Study in the Geometry of Meromorphic Connections (Lecture Notes in Mathematics) (en Inglés)
Price: 54460.00 CLP
Availability: InStock
Author: Guest,Hertling
ISBN: 9783319665252

portada Painlevé Iii: A Case Study in the Geometry of Meromorphic Connections (Lecture Notes in Mathematics) (en Inglés)

Formato

Libro Físico

Editorial

Springer

Autor

Guest,Hertling

Año

2017

Idioma

Inglés

N° páginas

204

Encuadernación

Tapa Blanda

ISBN13

9783319665252

Categorías

Cálculo diferencial y ecuaciones

Painlevé Iii: A Case Study in the Geometry of Meromorphic Connections (Lecture Notes in Mathematics) (en Inglés)

Guest,Hertling (Autor) · Springer · Tapa Blanda

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Reseña del libro "Painlevé Iii: A Case Study in the Geometry of Meromorphic Connections (Lecture Notes in Mathematics) (en Inglés)"

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 all zeros and poles of all real solutions of PIII (0, 0, 4, ?4) on R>0 is given.