Skip to main content
  • Book
  • © 2013

Introduction to Stokes Structures

Authors:

  • 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)

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

This is a preview of subscription content, access via your institution.

Table of contents (15 chapters)

  1. Front Matter

    Pages i-xiv
  2. Back Matter

    Pages 239-249

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.

Keywords

  • 34M40, 32C38, 35A27
  • Meromorphic connection
  • Stokes filtration
  • Stokes-perverse sheaf
  • real blowing-up
  • ordinary differential equations
  • partial differential equations

Authors and Affiliations

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

    Claude Sabbah

Bibliographic Information

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions