On the generalized Riemann–Hilbert problem with irregular singularities
Copyright policy )On the generalized Riemann–Hilbert problem with irregular singularities
We give sufficient conditions, on data including the monodromy representation, the Stokes matrices and the Poincare ranks at prescribed singularities, to solve the generalized Riemann-Hilbert problem with irregular singularities. We recover in particular the irreducibility condition on the monodromy given by Bolibrukh and Kostov in the classical case. We apply the above criteria to solve the inverse problem in differential Galois theory with a better control of the singularities.
- Centre national de la recherche scientifique France
- UNIVERSITE DE LILLE I France
- University of Lille France
- Université de Lille 2 France
- Institut de Recherche Mathématique Avancée France
Mathematics(all), 20G15, 34M50; 34M25; 34M35; 34M40; 20G15, Stokes matrices, 34M40, Differential algebra, 34M35, Mathematics - Algebraic Geometry, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Poincaré rank, Algebraic Geometry (math.AG), Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain, Riemann-Hilbert problem, Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain, Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms, Holomorphic vector bundles, linear ordinary differential equations, monodromy, Connections, 34M50, connections, holomorphic vector bundles, 34M25, Holomorphic bundles and generalizations, Mathematics - Classical Analysis and ODEs, Monodromy, Linear algebraic groups over the reals, the complexes, the quaternions, Linear ordinary differential equations
Mathematics(all), 20G15, 34M50; 34M25; 34M35; 34M40; 20G15, Stokes matrices, 34M40, Differential algebra, 34M35, Mathematics - Algebraic Geometry, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Poincaré rank, Algebraic Geometry (math.AG), Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain, Riemann-Hilbert problem, Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain, Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms, Holomorphic vector bundles, linear ordinary differential equations, monodromy, Connections, 34M50, connections, holomorphic vector bundles, 34M25, Holomorphic bundles and generalizations, Mathematics - Classical Analysis and ODEs, Monodromy, Linear algebraic groups over the reals, the complexes, the quaternions, Linear ordinary differential equations
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