Galois Theory of Linear Differential Equations

Marius Van der Put, Michael F. Singer

456 pages, parution le 29/01/2003

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Résumé

Linear differential equations form the central topic of this volume, Galois theory being the unifying theme.

A large number of aspects are presented: algebraic theory especially differential Galois theory, formal theory, classification, algorithms to decide solvability in finite terms, monodromy and Hilbert's 21st problem, asymptotics and summability, the inverse problem and linear differential equations in positive characteristic. The appendices aim to help the reader with concepts used, from algebraic geometry, linear algebraic groups, sheaves, and tannakian categories that are used.

This volume will become a standard reference for all mathematicians in this area of mathematics, including graduate students.

Keywords: Arithmetic, Asymptotics, Computer Algebra, Direct Problems, Galois Theory, Global Classification, Inverse Problems, Linear Differential Equations, Local Classification

Contents

Picard-Vessiot Theory
Differential Operators and Differential Modules
Formal Local Theory
Algorithmic Considerations
Monodromy, the Riemann-Hilbert Problem, and the Differential Galois Group
Differential Equations on the Complex Sphere and the Riemann-Hilbert Problem
Exact Asymptotics
Stokes Phenomenon and Differential Galois Groups
Stokes Matrices and Meromorphic Classification
Universal Picard-Vessiot Rings and Galois Groups
Inverse Problems
Moduli for Singular Differential Equations
Positive Characteristic

Appendices

A Algebraic Geometry
B Tannakian Categories
C Sheaves and Cohomology
D Partial Differential Equations

L'auteur - Marius Van der Put

University of Groningen, The Netherlands

L'auteur - Michael F. Singer

North Carolina State University, Raleigh, NC, USA

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Marius Van der Put, Michael F. Singer
Parution	29/01/2003
Nb. de pages	456
Format	16 x 24
Couverture	Relié
Poids	793g
Intérieur	Noir et Blanc
EAN13	9783540442288