publication . Doctoral thesis . 2016

Équations d'isomonodromie, solutions algébriques et dynamique

Girand, Arnaud;
Open Access English
  • Published: 31 Aug 2016
  • Publisher: HAL CCSD
Abstract
We call isomonodromic deformation any family of logarithmic flat connections over a punctured sphere having the same monodromy representation up to global conjugacy. These objects are parametrised by the solutions of a particular family of partial differential equations called Garnier systems, which are equivalent to the Painlevé VI equations in the four punctured case. The purpose of this thesis is to construct new algebraic solutions of these systems in the five punctured case. First, we give a classification of algebraic isomonodromic deformations obtained by restricting to lines some logarithmic flat connection over the complex projective plane whose singula...
Subjects
free text keywords: Isomonodromic deformations, logarithmic flat connections, transversaly projective foliations, Garnier Systems, Katz's middle convolution, convolution intermédiaire de Katz, systèmes de Garnier, feuilletages transversallement projectifs, déformations isomonodromiques, connexions logarithmiques plates, [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV], [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [ MATH.MATH-CV ] Mathematics [math]/Complex Variables [math.CV], [ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG], [ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS]
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publication . Doctoral thesis . 2016

Équations d'isomonodromie, solutions algébriques et dynamique

Girand, Arnaud;