P3D6-TEP Bundles

Martin Guest; Claus Hertling

doi:10.1007/978-3-319-66526-9_6

P_3D6-TEP Bundles

Martin Guest^*, Claus Hertling

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

In this monograph we are interested in the Painlevé III(D ₆) equation of type (α, β, γ, δ) = (0, 0, 4, −4) and in the isomonodromic families of P_3D6 bundles which are associated to it in [FN80, IN86, FIKN06, Ni09]. These P_3D6 bundles are special and can be equipped with rich additional structure. We shall develop this structure in two steps in Chaps. 6 and 7 The most important part is the TEP structure below. In Chap. 7 it will be further enriched to a TEJPA structure. Isomonodromic families of P_3D6-TEJPA bundles will correspond to solutions of the equation P_III(0, 0, 4, −4) (Theorem 10.3).

Original language	English
Title of host publication	Lecture Notes in Mathematics
Publisher	Springer Verlag
Pages	49-57
Number of pages	9
Volume	2198
DOIs	https://doi.org/10.1007/978-3-319-66526-9_6
Publication status	Published - 2017

Publication series

Name	Lecture Notes in Mathematics
Volume	2198
ISSN (Print)	0075-8434

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1007/978-3-319-66526-9_6

Cite this

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title = "P3D6-TEP Bundles",

abstract = "In this monograph we are interested in the Painlev{\'e} III(D 6) equation of type (α, β, γ, δ) = (0, 0, 4, −4) and in the isomonodromic families of P3D6 bundles which are associated to it in [FN80, IN86, FIKN06, Ni09]. These P3D6 bundles are special and can be equipped with rich additional structure. We shall develop this structure in two steps in Chaps. 6 and 7 The most important part is the TEP structure below. In Chap. 7 it will be further enriched to a TEJPA structure. Isomonodromic families of P3D6-TEJPA bundles will correspond to solutions of the equation PIII(0, 0, 4, −4) (Theorem 10.3).",

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AB - In this monograph we are interested in the Painlevé III(D 6) equation of type (α, β, γ, δ) = (0, 0, 4, −4) and in the isomonodromic families of P3D6 bundles which are associated to it in [FN80, IN86, FIKN06, Ni09]. These P3D6 bundles are special and can be equipped with rich additional structure. We shall develop this structure in two steps in Chaps. 6 and 7 The most important part is the TEP structure below. In Chap. 7 it will be further enriched to a TEJPA structure. Isomonodromic families of P3D6-TEJPA bundles will correspond to solutions of the equation PIII(0, 0, 4, −4) (Theorem 10.3).

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