Introduction to Stokes Structures

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...

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Bibliographic Details
Main Author: Sabbah, Claude. (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
Series:Lecture Notes in Mathematics, 2060
Subjects:
Online Access:https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-31695-1
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520 # # |a 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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650 # 0 |a Geometry, algebraic. 
650 # 0 |a Differential Equations. 
650 # 0 |a Differential equations, partial. 
650 # 0 |a Sequences (Mathematics). 
650 1 4 |a Mathematics. 
650 2 4 |a Algebraic Geometry. 
650 2 4 |a Ordinary Differential Equations. 
650 2 4 |a Approximations and Expansions. 
650 2 4 |a Sequences, Series, Summability. 
650 2 4 |a Several Complex Variables and Analytic Spaces. 
650 2 4 |a Partial Differential Equations. 
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