BIBFRAME Work

Title

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

Type

  • Monograph
  • Text

Contribution

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Content

Summary

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 typePIII (D6), calledPIII (0, 0, 4, -4), describing its relation to isomonodromic families of vector bundles onP1with 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 onR>0 (with or without singularities) are addressed. These provide examples of variations of TERP structures, which are related tott*geometry and harmonic bundles. As an application, a new global picture of0 is given.

Table of Contents

1. Introduction -- 2.-The Riemann-Hilbert correspondence for P3D6 bundles -- 3.(Ir)Reducibility -- 4. Isomonodromic families -- 5. Useful formulae: three 2 x 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.

Authorized Access Point

Guest, Martin A. Painlevé III: A Case Study in the Geometry of Meromorphic Connections

Admin Metadata

  • Date: 2026-09-11T20:16:06.394970+00:00
  • Agent: cbc
  • Status: c
  • Derived from: 21580463

Admin Metadata

  • Date: 2026-09-11
  • Cataloger id: Unknown
  • Description level: http://id.loc.gov/ontologies/bibframe-2-6-0/
  • Description language: eng
  • Description authentication: pcc

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