Rank reduction, normal forms and Stokes matrices

DOI10.1016/S0723-0869(01)80003-7zbMath0990.34076OpenAlexW2010685449MaRDI QIDQ5947329

Michèle Loday-Richaud

Publication date: 5 August 2002

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0723-0869(01)80003-7

zbMATH Keywords

\(K\)-connectionformal fundamental solutionmeromorphic classificationPoincaré rankStokes matrices

Mathematics Subject Classification ID

Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25) Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain (34M40)

Related Items (8)

Monomial summability and doubly singular differential equations ⋮ Multi-resurgence and connection-to-Stokes formulæ for some linear meromorphic differential systems ⋮ Resurgence and highest level's connection-to-Stokes formulæ for some linear meromorphic differential systems ⋮ Resurgence, Stokes phenomenon and alien derivatives for level-one linear differential systems ⋮ Stokes-Ramis matrices and connection constants for linear differential systems with a single level ⋮ Resurgence-summability of ramified formal series depending of a parameter and solutions of linear differential equations ⋮ On the generalized Riemann--Hilbert problem with irregular singularities ⋮ Automatic computation of Stokes matrices

Cites Work

• On the reduction of rank of linear differential systems
• Formal reduction theory of meromorphic differential equations: a group theoretic view
• Lemmes de Hensel pour les opérateurs différentiels. Application à la reduction formelle des équations différentielles
• Transfer of connection problems for meromorphic differential equations of rank \(r\geq 2\) and representations of solutions
• Stokes phenomenon, multisummability and differential Galois groups
• Reducing the rank of ordinary differential equations
• Convergent solutions of ordinary linear homogeneous differential equations in the neighborhood of an irregular singular point
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