Introduction to Stokes Structures
By: by Claude Sabbah
Contributors: SpringerLink (Online service)
Series: Lecture Notes in Mathematics -- 2060
Publisher: Springer Berlin Heidelberg; Imprint: Springer
Published: 2013
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 249
ISBN-13: 9783642316951
Subjects: Differential equations; Sequences, Series, Summability; Approximations and Expansions; Ordinary Differential Equations; Algebraic Geometry; Partial Differential equations; Mathematics; Several Complex Variables and Analytic Spaces; Sequences (Mathematics)
Description: 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.<br>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.