Introduction to Stokes Structures

This research monograph provides a geometric description of holonomic differential systems in one or more variables. Stokes matrices form the extended monodromy data for a linear differential equation of one complex variable near an irregular singular point. The present volume presents the approach in terms of Stokes filtrations. For linear differential equations on a Riemann surface, it also develops the related notion of a Stokes-perverse sheaf.This point of view is generalized to holonomic systems of linear differential equations in the complex domain, and a general Riemann-Hilbert correspondence is proved for vector bundles with meromorphic connections on a complex manifold. Applications to the distributions solutions to such systems are also discussed, and various operations on Stokes-filtered local systems are analyzed.

Summary

This research monograph provides a geometric description of holonomic differential systems in one or more variables. Stokes matrices form the extended monodromy data for a linear differential equation of one complex variable near an irregular singular point. The present volume presents the approach in terms of Stokes filtrations. For linear differential equations on a Riemann surface, it also develops the related notion of a Stokes-perverse sheaf.
This point of view is generalized to holonomic systems of linear differential equations in the complex domain, and a general Riemann-Hilbert correspondence is proved for vector bundles with meromorphic connections on a complex manifold. Applications to the distributions solutions to such systems are also discussed, and various operations on Stokes-filtered local systems are analyzed.

Product details

• Authors: Claude Sabbah
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 08.06.2012
• EAN: 9783642316944
• ISBN: 978-3-642-31694-4
• No. of pages: 249
• Dimensions: 156 mm x 15 mm x 237 mm
• Weight: 418 g
• Illustrations: XIV, 249 p. 14 illus., 1 illus. in color.
• Series: Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Analysis, B, Mathematics and Statistics, Algebraic Geometry, Ordinary Differential Equations, Partial Differential Equations, Complex analysis, complex variables, Differential calculus & equations, Differential equations, Sequences, Series, Summability, Calculus & mathematical analysis, Sequences (Mathematics), Functions of complex variables, Several Complex Variables and Analytic Spaces, Approximations and Expansions, Approximation theory