Solvability of linear differential systems with small exponents in the Liouvillian sense

DOI10.1007/s40598-015-0032-4zbMath1339.34091OpenAlexW2288416973WikidataQ112879773 ScholiaQ112879773MaRDI QIDQ5964207

I. V. V'yugin, Renat Gontsov

Publication date: 29 February 2016

Published in: Arnold Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40598-015-0032-4

zbMATH Keywords

differential Galois groupStokes matricesLiouvillian solutionPicard-Vessiot extension

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) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15) Linear ordinary differential equations and systems in the complex domain (34M03)

Related Items

On the dimension of the subspace of Liouvillian solutions of a Fuchsian system ⋮ Reduction of Schlesinger systems to linear Jordan-Pochhammer systems ⋮ Linear differential systems with small coefficients: various types of solvability and their verification

Cites Work

• Stokes phenomenon, multisummability and differential Galois groups
• Differential Galois groups of confluent generalized hypergeometric equations: An approach using Stokes multipliers
• Topological obstructions to the representability of functions by quadratures.
• On the generalized Riemann--Hilbert problem with irregular singularities
• Algebraic matric groups and the Picard-Vessiot theory of homogeneous linear ordinary differential equations
• Relations de Fuchs pour les systèmes différentiels réguliers
• Picard-Vessiot Extensions of Real Differential Fields
• Various versions of the Riemann-Hilbert problem for linear differential equations
• Invariants for reducible systems of meromorphic differential equations
• Refined Fuchs inequalities for systems of linear differential equations
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