Introduction to stokes structures

Introduction to stokes structures

by Sabbah, Claude

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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 …

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Title Statements

  • Full title :Introduction to stokes structures / Claude Sabbah.

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.

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Edition Statements

  • Publication Date:©2013.

Publication Statements

  • Publisher(s):Springer
  • Place of Publication:Berlin
  • Language:eng
  • Publication Date:©2013.

The Physical Object

  • Description:1 online resource (xiv, 249 pages) : : illustrations

Edition Identifiers

  • ISBN:3642316956, 9783642316951
  • DOI:10.1007/978-3-642-31695-1
  • oclc:ocn812138227
  • LC Classification:QA371
  • Dewey Decimal:515/.354

Subjects

Differential equations, Linear Équations différentielles linéaires Stoke's theorem Stokes-Phänomen Théorème de Stokes

Writers

Sabbah, Claude

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