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Isomonodromic deformations through differential Galois theory

Abstract : The text begins with a brief description of differential Galois theory from a geometrical perspective. Then, parameterized Galois theory is developed by means of prolongation of partial connections to the jet bundles. The relation between the parameterized differential Galois groups and isomonodromic deformations is unfold as an application of Kiso-Cassidy theorem. It follows the computation of the parameterized Galois groups of the general fuchsian equation and Gauss hypergeometric equation. Finally, some non-linear applications are developed. By means of a non-linear analog, Kiso-Morimoto theorem, the Malgrange groupoid of Painlevé VI equation with variable parameters is calculated.
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Contributor : Juan Sebastián Díaz Arboleda <>
Submitted on : Tuesday, June 9, 2020 - 10:48:41 PM
Last modification on : Friday, July 10, 2020 - 4:05:03 PM

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  • HAL Id : tel-02338314, version 2

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Juan Sebastián Díaz Arboleda. Isomonodromic deformations through differential Galois theory. Differential Geometry [math.DG]. Université de Rennes 1; Universidad Nacional de Colombia, 2019. English. ⟨tel-02338314v2⟩

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