Monodromy groups of parameterized linear differential equations with regular singularities

DOI10.1112/blms/bds021zbMath1254.34124arXiv1106.2664OpenAlexW3103772451WikidataQ57430355 ScholiaQ57430355MaRDI QIDQ2918785

Michael F. Singer, Claude Mitschi

Publication date: 10 October 2012

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.2664

zbMATH Keywords

monodromy groupdifferential Galois groupPicard-Vessiot theory(weak) Riemann-Hilbert Problemsystem of ordinary linear differential equations on Riemann's sphere

Mathematics Subject Classification ID

Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Differential algebra (12H05) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50) Isomonodromic deformations for ordinary differential equations in the complex domain (34M56)

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Unipotent differential algebraic groups as parameterized differential Galois groups ⋮ Calculating differential Galois groups of parametrized differential equations, with applications to hypertranscendence ⋮ Calculating Galois groups of third-order linear differential equations with parameters ⋮ Parameterized Picard-Vessiot extensions and Atiyah extensions ⋮ Existence of \(\partial\)-parameterized Picard-Vessiot extensions over fields with algebraically closed constants ⋮ New classes of parameterized differential Galois groups ⋮ Computation of the difference-differential Galois group and differential relations among solutions for a second-order linear difference equation ⋮ DIFFERENCE ALGEBRAIC RELATIONS AMONG SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS ⋮ Difference Galois theory of linear differential equations ⋮ Isomonodromic differential equations and differential categories ⋮ Algebraic groups as difference Galois groups of linear differential equations ⋮ On the parameterized differential inverse Galois problem over \(k((t))(x)\) ⋮ Spectral Picard-Vessiot fields for algebro-geometric Schrödinger operators

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