Cover Image

Galois Theory of Linear Differential Equations /

Show other versions (1)

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...

Full description

Bibliographic Details
Main Author: Put, Marius
Corporate Author: SpringerLink (Online service)
Other Authors: Singer, Michael F.
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint : Springer, 2003.
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, ; 328.
Subjects:
Mathematics.
Geometry, Algebraic.
Algebra.
Differential equations.
Number theory.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Algebraic Theory: Picard-Vessiot Theory
  • Differential Operators and Differential Modules
  • Formal Local Theory
  • Algorithmic Considerations Analytic Theory: 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: Algebraic Geometry
  • Tannakian Categories
  • Sheaves and Cohomology
  • Partial Differential Equations.