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Introduction to Stokes Structures

  • Book
  • © 2013

Overview

  • A first part on the classical theory of linear differential equations in the complex domain revisited from a geometric view point.
  • Original and new study of the Stokes phenomenon in higher dimension.
  • Application to classical problems in distribution theory.
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2060)

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Table of contents (15 chapters)

Keywords

About this book

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.

Authors and Affiliations

  • Centre de mathématiques, CNRS Ecole polytechnique, Palaiseau, France

    Claude Sabbah

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