### 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 |
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Title of host publication | Lecture Notes in Mathematics |

Publisher | Springer Verlag |

Pages | 49-57 |

Number of pages | 9 |

Volume | 2198 |

DOIs | |

Publication status | Published - 2017 |

### Publication series

Name | Lecture Notes in Mathematics |
---|---|

Volume | 2198 |

ISSN (Print) | 0075-8434 |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

_{3D6}-TEP Bundles. In

*Lecture Notes in Mathematics*(Vol. 2198, pp. 49-57). (Lecture Notes in Mathematics; Vol. 2198). Springer Verlag. https://doi.org/10.1007/978-3-319-66526-9_6

**P _{3D6}-TEP Bundles.** / Guest, Martin; Hertling, Claus.

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

_{3D6}-TEP Bundles. in

*Lecture Notes in Mathematics.*vol. 2198, Lecture Notes in Mathematics, vol. 2198, Springer Verlag, pp. 49-57. https://doi.org/10.1007/978-3-319-66526-9_6

_{3D6}-TEP Bundles. In Lecture Notes in Mathematics. Vol. 2198. Springer Verlag. 2017. p. 49-57. (Lecture Notes in Mathematics). https://doi.org/10.1007/978-3-319-66526-9_6

}

TY - CHAP

T1 - P3D6-TEP Bundles

AU - Guest, Martin

AU - Hertling, Claus

PY - 2017

Y1 - 2017

N2 - 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).

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).

UR - http://www.scopus.com/inward/record.url?scp=85032018691&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85032018691&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-66526-9_6

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

M3 - Chapter

AN - SCOPUS:85032018691

VL - 2198

T3 - Lecture Notes in Mathematics

SP - 49

EP - 57

BT - Lecture Notes in Mathematics

PB - Springer Verlag

ER -