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Introduction to Stokes Structures
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Artikel-Nr:
9783642316944
Veröffentl:
2012
Einband:
Paperback
Erscheinungsdatum:
04.10.2012
Seiten:
268
Autor:
Claude Sabbah
Gewicht:
411 g
Format:
235x155x15 mm
Serie:
2060, Lecture Notes in Mathematics
Sprache:
Englisch
Beschreibung:
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.
A first part on the classical theory of linear differential equations in the complex domain revisited from a geometric view point.