Description 
1 online resource (xiv, 249 pages) : illustrations 
Series 
Lecture notes in mathematics, 16179692 ; 2060 

Lecture notes in mathematics (SpringerVerlag) ; 2060.

Contents 
IFiltrations  StokesFiltered Local Systems in Dimension One  Abelianity and Strictness  StokesPerverse Sheaves on Riemann Surfaces  The RiemannHilbert Correspondence for Holonomic Modules on Curves  Applications of the RiemannHilbert Correspondence to Holonomic Distributions  RiemannHilbert and Laplace on the Affine Line (the Regular Case)  Real BlowUp Spaces and Moderate de Rham Complexes  StokesFiltered Local Systems Along a Divisor with Normal Crossings  The RiemannHilbert Correspondence for Good Meromorphic Connections (Case of a Smooth Divisor)  Good Meromorphic Connections (Formal Theory)  Good Meromorphic Connections (Analytic Theory) and the RiemannHilbert Correspondence  PushForward of StokesFiltered Local Systems  Irregular Nearby Cycles  Nearby Cycles of StokesFiltered Local Systems 
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 Stokesperverse sheaf. This point of view is generalized to holonomic systems of linear differential equations in the complex domain, and a general RiemannHilbert 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 Stokesfiltered local systems are analyzed 
Bibliography 
Includes bibliographical references and index 
Notes 
English 

Online resource; title from PDF title page (SpringerLink, viewed October 8, 2012) 
Subject 
Differential equations, Linear.


Stokes' theorem.


Differential equations, Linear.


Stokes' theorem.


StokesPhänomen

Genre/Form 
Electronic books

Form 
Electronic book

ISBN 
3642316956 

9783642316951 
